Relativistic Effects in Heavy-Element Chemistry and...

Relativistic Effectsin Heavy-Element Chemistry and Physics

Relativistic Quantum Chemistry -Progress and Prospects

Chairman: Jaap G. Snijders (Groningen)Vice-Chairman: Ian P. Grant (Oxford)

P r o g r a m m e A b s t r a c t s

P a r t i c i p a n t s

Acquafredda di Maratea, Italy10-15 April 1999

Edited by Johan J. Heijnen (Groningen)

3

Relativistic Effectsin Heavy-Element Chemistry and Physics

Relativistic Quantum Chemistry -Progress and Prospects

Chairman: Jaap G. Snijders (Groningen)Vice-Chairman: Ian P. Grant (Oxford)

P r o g r a m m e A b s t r a c t s

P a r t i c i p a n t s

Acquafredda di Maratea, Italy10-15 April 1999

Edited by Johan J. Heijnen (Groningen)

5

Contents

Preface 7

Programme 9

Speakers 15

Speaker Abstracts 17

Poster presenters 45

Poster Abstracts 49

Participants 97

7

Preface

This European Research Conference has been convened to present, review and discussrecent advances in the theoretical methods developed for treating relativistic effects inatoms. molecules and solids and to relate them to recent experimental work. The talksand posters whose abstracts appear in this booklet reflect the wide range of work inprogress in the countries of the European Union, as well as the contributions fromlaboratories in the rest of the world. An encouraging number of the contributions involvethe participation of the young researchers on whom the future of this field depends.

With your participation, we look forward to a lively and stimulating conference.

JGSIPG

9

Programme

Saturday, April 10

Arrival

Afternoon Registration

20.00 DINNER

21.30 GET TOGETHER DRINKS

10

Sunday, April 11, Session Relativistic Effects in Chemistry

7.30 BREAKFAST

8.50 Jaap Snijders (Groningen, The Netherlands)Opening remarks

Chair: Jaap Snijders (Groningen, The Netherlands)

9.00 Pekka Pyykkö (Helsinki, Finland)Relativistic quantum chemistry: Recent results

10.00 D. Michael Mingos (London, United Kingdom)An experimentalist’s view of relativistic effects in chemistry and specificallyaurophilicity

10.35 COFFEE

Chair: Christian Teichteil (Toulouse, France)

11.10 Hubert Schmidbauer (Garching, Germany)Gold: From alchemy to relativity and back

11.45 Jan Hrusak (Prague, Czech Republic)Ab initio and DFT calculations on Gold containing systems

12.20 Angela Rosa (Potenza, Italy)Structural properties of molecular metals.Insights from relativistic density functional calculations

12.55 LUNCH

15.00 COFFEE

Chair: Evert-Jan Baerends (Amsterdam, The Netherlands)

15.30 Chantal Daniel (Strassbourg, France)Coordination compounds photochemistry:Spin-orbit effects on the photodissociation dynamics

16.05 Knut Fægri (Oslo, Norway)Four-component relativistic calculations at work.

16.40 W.H. Eugen Schwarz (Siegen, Germany)Chemical bonding and the Hellmann-Feynman theorem in relativisticquantum chemistry

17.15 Poster Session I (P01-P30)

20.00 DINNER

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Monday, April 12, Session Relativistic Computational Methods

7.30 BREAKFAST

Chair: Knut Fægri (Oslo, Norway)

9.00 Bernd Heß (Erlangen, Germany)Transformed Hamiltonians for relativistic electronic structure calculations

10.00 Maria Barysz (Torun, Poland)The 2 accuracy and beyond

10.35 COFFEE

Chair: Werner Kutzelnigg (Bochum, Germany)

11.10 Joop van Lenthe (Utrecht, The Netherlands)The ZORA approach in ab initio quantum chemistry

11.45 Ulf Wahlgren (Stockholm, Sweden)Relativistic calculations on actinyl complexes.

12.20 Sten Rettrup (Copenhaguen, Denmark)The symmetric group approach to spin-dependent properties

12.55 LUNCH

15.00 COFFEE

Chair: Luuk Visscher (Amsterdam, The Netherlands)

15.30 Uzi Kaldor (Tel Aviv, Israel)Four-component relativistic coupled-cluster method

16.05 Harry Quiney (Parkville, Australia)Ab initio four-component relativistic electronic structure calculationsusing BERTHA

16.40 Paolo Palmieri (Bologna, Italy)Improved Configuration Interaction techniques for the evaluation of spin-orbitand spin-spin matrix elements and for theoretical analyses of the fine structure ofelectronic levels and molecular properties

17.15 Poster Session II (P31-P60)

20.00 DINNER

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Tuesday, April 13, Session Relativistic Effects in Spectroscopy

7.30 BREAKFAST

Chair: Andrzej Sadlej (Lund, Sweden and Torun, Poland)

9.00 Christel Marian (Bonn, Germany)Relativistic effects in molecular spectroscopy: Case studies

10.00 John Dyke (Southampton, United Kingdom)Relativistic effects in the photoionization and photoexcitation of short-lived atomsand molecules

10.35 COFFEE

Chair: Michel Godefroid (Brussels, Belgium)

11.10 Tommi Matila (Oulu, Finland)Vibrational and electronic structure of the normal Auger spectrum of HBr studiedby fully relativistic configuration interaction calculations

11.45 Charlotte Froese Fischer (Nashville, United States of America)Correlation and relativistic effects in lighter atoms

12.20 Erik van Lenthe (Amsterdam, The Netherlands)Density functional calculations of molecular properties in the zero order regularapproximation for relativistic effects

12.55 LUNCH

14.00 Excursion

20.00 CONFERENCE DINNER

Wim Nieuwpoort (Groningen, The Netherlands)Relativity After Dinner

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Wednesday, April 14, Session Relativistic Effects in Atomic Physics and QED

7.30 BREAKFAST

Chair: Gulzari Malli (Burnaby, Canada)

9.00 Vladimir Shabaev (St. Petersburg, Russia)QED effects in high-Z few-electron atoms

10.00 Thomas Beier (Göteborg, Sweden)QED effects in highly charged ionsThe g-factor of the bound electron as an example

10.35 COFFEE

Chair: Pekka Pyykkö, (Helsinki Finland)

11.10 Jacek Bieron (Krakow, Poland)Complete active space in Dirac-Fock theory

11.45 Edward Hinds (Brighton, United Kingdom)YbF: a new laboratory for elementary particle physics.

12.20 Ann-Marie Mårtensson-Pendrill (Göteborg, Sweden)Atoms through the looking glass

12.55 LUNCH

15.00 COFFEE

Chair: Ian Grant (Oxford, United Kingdom)

15.30 Anatoli Titov (St. Petersburg, Russia)GRECP method and procedures of electronic structure

restoration in cores of heavy-atom systems

16.05 Ian Grant (Oxford, United Kingdom)Gazing in the crystal ball

20.00 DINNER

14

Thursday, April 14

7.30 BREAKFAST

Departure

15

Speakersalphabetic order, with abstract number

S01 Maria Barysz, Torun, Poland, [email protected] α2 accuracy and beyond it

S02 Thomas Beier, Göteborg, Sweden, [email protected] effects in highly charged ions - The g-factor of the bound electron as an example

S03 Jacek Bieron, Krakow, Poland, [email protected] active space in Dirac-Fock theory

S04 Chantal Daniel, Strasbourg, France, [email protected] Compounds Photochemistry: Spin-Orbit Effects on the PhotodissociationDynamics

S05 John M. Dyke, Southampton, United Kingdom, [email protected] Effects in the Photoionization and Photoexcitation of Short-Lived Atoms andMolecules

S06 Knut Fægri, Oslo, Norway, [email protected] relativistic calculations at work.

S07 Charlotte Froese Fischer, Nashville , USA, [email protected] and relativistic effects in lighter atoms

S08 Ian Grant, Oxford, United Kingdom, [email protected] in the crystal ball

S09 Bernd A. Heß, Erlangen, Germany, [email protected] Hamiltonians for Relativistic Electronic-Structure Calculations

S10 Ed A. Hinds, Brighton, UK, [email protected]: a new laboratory for elementary particle physics

S11 Jan Hrusak, Prague, Czech Republic, [email protected] initio and DFT calculations on coinage metal containing systems

S12 Uzi Kaldor, Tel Aviv, Israel, [email protected] relativistic coupled-cluster method

S13 Christel M. Marian, Bonn, Germany, [email protected] Effects in Molecular Spectroscopy: Case Studies

S14 Tommi Matila, Oulu, Finland,[email protected] and electronic structure of the normal Auger spectrum of HBr studied by fullyrelativistic configuration interaction calculations

S15 D. Michael P. Mingos, London, United Kingdom, [email protected] Experimentalist’s View of Relativistic Effects in Chemistry and Specifically Aurophilicity

S16 Wim Nieuwpoort, Groningen, The Netherlands, [email protected] After Dinner

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S17 Paolo Palmieri, Bologna, Italy, [email protected] Configuration Interaction Techniques for the evaluation of spin-orbit and spin-spinmatrix elements and for theoretical analyses of the fine structure of electronic levels andmolecular properties

S18 Ann-Marie Mårtensson-Pendrill, Göteborg, Sweden, [email protected] through the looking glass

S19 Pekka Pyykkö, Helsinki, Finland, [email protected] quantum chemistry: Recent results.

S20 Harry Quiney, Melbourne, Australia, [email protected] initio four-component relativistic electronic structure calculations using BERTHA

S21 Sten Rettrup, Copenhagen, Denmark, [email protected] Symmetric Group Approach to Spin-Dependent Properties

S22 Angela Rosa, Potenza, Italy, [email protected] Properties of M(dmit)2(M = Ni, Pd, Pt, dmit2- = 2-Thioxo-1,3-dithiole-4,5-dithiolato) Based Molecular Metals. Insights from Relativistic Density FunctionalCalculations

S23 Hubert Schmidbaur, Garching, Germany, [email protected] Chemistry: From Alchemy to Relativity and Back

S24 Eugen Schwarz, Siegen, Germany, [email protected] Bonding and the Hellmann-Feynman Theorem in Relativistic Quantum Chemistry

S25 Vladimir Shabaev, St.Petersburg, Russia, [email protected] effects in high-Z few-electron atoms

S26 Jaap G. Snijders, Groningen, The Netherlands, [email protected] remarks

S27 Anatoli Titov, St. Petersburg, Russia, [email protected] method and procedures of electronic structure restoration in cores of heavy-atomsystems

S28 Erik van Lenthe, Amsterdam, The Netherlands, [email protected] functional calculations of molecular properties in the zero order regularapproximation for relativistic effects

S29 Joop H. van Lenthe, Utrecht, The Netherlands, [email protected] ZORA approach in Ab Initio Quantumchemistry

S30 Ulf Wahlgren, Stockholm, Sweden, [email protected] calculations on actinyl complexes

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Speaker Abstracts

18

S01

The 2 accuracy and beyond it

Maria Barysz

Department of Quantum Chemistry, Institute of Chemistry,Nicolaus Copernicus University, Torun, Poland

The α2-order methods of the relativistic quantum chemistry are the easiest theoretical toolto account for the relativistic effect on the electronic structure of atoms and molecules. Aslong as the energy calculations are concerned such methods exhaust all relativistic effectsthrough the second-order in the fine structure constant. However, most of subsequentproperty calculations, which are usually carried out in terms of the expectation values ofthe appropriate (Schrödinger) operator, can be shown to miss some part of the α2 terms.The recognition of the error involved in this commonly used approximation is also ofimportance for the discussion of the relativistic effect on bond length and relatedproperties.In recent years a great deal of interest has been given to methods which go beyond the α2-order of approximation in relativistic terms. Among new methods, which can possibly beused in the variational framework, an open-ended formulation of two- and one-component relativistic theories, has been proposed. At variance with the very successfulDouglas-Kroll approximation the new method permits an easy extension to arbitrarilyhigh order in α2, and thus, can be used for very heavy elements. The performance of thismethod at different levels of accuracy with respect to α2 will be discussed and illustrated.

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S02

QED effects in highly charged ionsThe g-factor of the bound electron as an example

Thomas Beier

Department of Physics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden.

Among the testing fields of quantum electrodynamics, the g-factor of the free electron isfamous for its experimental and theoretical precision. Currently, work is undertaken tomeasure the g-factor of the bound electron in hydrogenlike systems. We will discuss therecent experimental results and the theoretical work carried out so far, and we willemphasize on the particular advantages of the g-factor calculations and experimentscompared to the Lamb shift and hyperfine structure splitting.

20

S03

Complete active space in Dirac-Fock theory

Jacek Bieron

Instytut FizykiUniwersytet Jagiellonski

Reymonta 4, 30-059 Kraków, Polandemail: [email protected]

Many-body perturbation theory and the variational methods often referred to as Hartree-Fock theory are the two dominant methods in present-day atomic-theory calculations.Both are designed to evaluate the electron correlation effects, the leading correction to theindependent-particle-model. The goal of this study is to systematically investigate thecomputation of atomic hyperfine structures within the framework of themulticonfiguration Dirac-Fock (MCDF) model.The configuration expansions were obtained with the active space method in whichconfiguration state functions of a particular parity and symmetry are generated bysubstitutions from reference configuration to an active set of orbitals. The active set isthen increased systematically until the convergence of the hyperfine constant is obtained.Several schemes were studied, where certain limitations are employed to keep the numberof configuration state functions below the limit acceptable by the computer memoryconstraints.An attempt has been made to extrapolate the systematic expansions of the active set, so asto achieve the level of approximation, which might be called an MCDF limit, bearing inmind, that this concept is somewhat more fuzzy than its nonrelativistic counterpart, andperhaps a "no-pair" MCDF limit would be a better description.Calculations of the hyperfine parameters were chosen as test cases. The calculatedmagnetic dipole hyperfine structure constants of several low-lying states of neutralLithium, Lithium-like Beryllium and the ground state of Lithium-like Fluorine will becompared with experiment and with values obtained by other theoretical methods. As thetest cases for moderately heavy systems, we have chosen the electric quadrupolehyperfine constants of several states of Sc+ and Y+ ions. The comparison of the calculatedhyperfine constants with experimentally determined hyperfine energy splittings yields thevalues of nuclear electromagnetic moments.

21

S04

Coordination Compounds Photochemistry: Spin-Orbit Effects on thePhotodissociation Dynamics

Chantal Daniel

Laboratoire de Chimie Quantique, UMR 7551 CNRS/ Université Louis Pasteur,Strasbourg, -F67000

The spin-orbit (SO) effects on the excited states dynamics of a number ofcoordination compounds is investigated through wavepackets propagations on SO coupledCASSCF/MR-CCI potentials calculated for the electronic ground state and the low-lyingexcited states involved in the photochemistry. The SO Coupling (SOC) induced mixingbetween the singlet and triplet electronic states is investigated through SOC-CI calculations,using a one-electron effective SO operator at the metal center. It is shown that the indirectdeactivation channel via singlet to triplet intersystem crossings is not competitive with theultra-fast direct deactivation via the low-lying singlet states directly populated undervertical excitation. The former mechanism occurs within a few tens of picoseconds (ps)whereas the latter one occurs within a few hundreds of femtoseconds (fs) in first- rowtransition metal complexes (HCo(CO)4, H2Fe(CO)4, HMn(CO)3(H-DAB) ; H-DAB= 1,4-diaza-1,3-butadiene). Consequently the nonradiationless transitions have a rather lowprobability indicating the minor role of the triplet states at the early satge of thephotodissociation. The SO effects on the photoreactivity of Metal-to-Ligand-Charge-Transfer (MLCT) complexes is illustrated by the study of the RM(CO)3(H-DAB) (M=Mn,Re ; R=H, ethyl) molecules. On the basis of the SO interactions calculated between the low-lying singlet and triplet n → π*DAB (MLCT) and σM-R → π*DAB (Sigma-Bond-to-Ligand-Charge-Transfer or SBLCT) excited states, it is shown how the SO effect may control themetal-R bond homolysis in this class of complexes. The photoreactivity (metal-R bondhomolysis or CO loss) is not only influenced by the SO interactions which range between0-100 cm-1 for M=Mn and between 100-800 cm-1 for M=Re or by the SO splitting of thetriplet states (a few tens of cm-1 for M=Mn and a few hundreds of cm-1 for M=Re), but alsoby the position of the critical geometries (singlet-triplet crossings) with respect to theFranck-Condon region and to the energy barriers occuring along the photodissociationpathways.

1 D. J.Stufkens, Comments Inorg. Chem. 13 (1992) 359. D. J. Stufkens, Coord. Chem. Rev.104 (1990) 39. H. V. van Dijk, Rossenaar, B. D.; van der Graaf, T.; van Eldik, R.Langford, C. H.; Stufkens, D. J.; Vlcek, A. Inorg. Chem. 33 (1994) 2865; Rossenaar, B.D.; Kleverlaan, C. J.; van de Ven, M. C. E.; Stufkens, D. J.; Vlcek, A. Chem. Eur. J. 2(1996) 228.

2. D. Guillaumont, K. Finger, M. R. Hachey, C. Daniel Coord.Chem. Rev. 171 (1998)439-459 , D. Guillaumont, C. Daniel. Coord. Chem. Rev., sous presse (1998), D.Guillaumont, M. P. Wilms, C. Daniel, D. J. Stufkens. Inorg. Chem. 37 (1998) 5816-5822 .

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S05

Relativistic Effects in the Photoionization and Photoexcitation of Short-Lived Atoms and Molecules

John M. Dyke

Department of ChemistryThe University

Southampton SO17 1BJUnited Kingdom

A review will be given of how relativistic effects have affected photoelectron and lasermultiphoton spectra, recorded in Southampton. Examples will be drawn from three areas,notably photoelectron spectra (PES) of atoms, PES of molecules and laser multiphotonionization (MPI) spectra of small molecules.

In the PES of atoms, the intensities and positions of the experimental bands dependsstrongly on the extent of spin-orbit coupling and an intermediate coupling model has beendeveloped to interpret the results obtained. Examples will be drawn from C, Si, Ge, Snand Pb, and F, Cl, Br and I.

In the PES of molecules, spin-orbit effects are observed in the valence region either asspin-orbit splitting of the ionic states involved or indirectly as second order spin-orbitsplittings from spin-orbit split inner valence or core ionic states. Examples discussedhere will include the interhalogens and uranium halides.

In laser multiphoton ionization spectra of reactive intermediates, spin-orbit effects oftenhave to be taken into account to interpret the rotationally resolved spectra obtained. Forexample, in the rotationally resolved two-photon transition of NF, 3Φ←a1∆, theexperimental band was found to derive its intensity from spin-orbit interaction of the 3Φstate with a nearby 1Φ state. Analysis of the rotationally resolved bands allowed thiseffect to be quantified.

23

S06

4-Component relativistic calculations at work.

Trond Saue and Knut Fægri

Kjemisk Institut, Oslo Universitetn Oslo, NorwayIRSAMC - LPQ , Universite Paul Sabatier, Toulouse, France

This talk presents 4-component relativistic molecular calculations based on the programpackage DIRAC (see http://dirac.chem.ou.dk/Dirac). Focus will be on chemistry,although some methodological aspects will be discussed. Research areas discussed coversactinide chemistry, NMR parameters, superheavy compounds and spin-orbit effects inclosed-shell molecules.

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S07

Correlation and relativistic effects in lighter atoms

Charlotte Froese Fischer

Vanderbilt University, Nashville TN 37235 USA

With the ever increasing speed of workstations and high-performance architectures, alongwith more efficient algorithms for angular integrations, considerable progress has beenmade in the accurate evaluation of atomic properties. But even for lighter atoms,relativistic effects need to be considered before a reliable comparison can be made withexperiment.Multiconfiguration variational techniques have been developed for both non-relativistic(MCHF) methods, with lowest order relativistic effects included in the Breit-Pauliapproximation, and fully relativistic (MCDF) methods with Breit and QED corrections.The Breit-Pauli approach is the simpler, less computationally intensive method, but insome instances even for lighter atoms, only MCDF is capable of capturing the relativisticcorrelation effect to the desired precision. In this talk, the two approaches will beevaluated and results compared for selected cases.

(Research supported by the Division of Chemical Sciences, Office of Basic EnergyScience, Office of Energy Research, US Department of Energy)

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S09

Transformed Hamiltonians for Relativistic Electronic-StructureCalculations

Bernd Artur Heß

Chair of Theoretical Chemistry, Friedrich-Alexander-Universität Erlangen-Nürnberg,Egerlandstr. 3, 91058 Erlangen, Germany;

e-mail: [email protected]

Under certain circumstances, the Dirac-Coulomb-Breit Hamiltonian, making use of four-component spinor wave functions, can be transformed to a representation in which largeand small components are decoupled. Freezing the charge-conjugated degrees offreedom, a two-component relativistic theory for the electrons obtains. The wave functioncan be further simplified by splitting the resulting Hamiltonian in a spin-dependent andspin-independent part, and solving the spin-independent problem before spin-orbitcoupling is included in the calculation. This leads to the so-called scalar relativisticmethods, featuring one-component wave functions.Early theories based on the Foldy-Wouthuysen transformation or the ''Elimination of theSmall Component'' lead to singular terms, rendering the use of the resulting ''Breit-Paulioperator'' dubious, at least in variational approaches.It is only in the last decade, that various regular transformation methods have beenformulated and made workable for relativistic molecular electronic structure calculations.I shall give an account of the corresponding theories and discuss in particular applicationsusing spin-free and spin-dependent operators obtained from a Douglas-Krolltransformation.

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Pump Split Recombine Probe

|0,0⟩|1,+1⟩

|1,−1⟩

E B

|0,0⟩

S10

YbF: a new laboratory for elementary particle physics

Ed A. Hinds, M. Kozlov, and B.E. Sauer

SCOAP, University of Sussex, Brighton BN1 9QH

The Ytterbium atom, having a filled f-shell ([Xe]4f146s2), resembles the alkaline earths and the grossfeatures of YbF resemble CaF, SrF or BaF. However, the spin-orbit interaction in YbF is much largerand there are some features associated with low-lying 4f hole configurations. As a heavy, polar,paramagnetic molecule, YbF is an extraordinarily sensitive system in which to detect an electric dipolemoment of the electron [1] and hence to search for new interactions beyond the standard model ofelementary particle physics.

Nearly half a century ago, it was recognised that an elementary particle cannot have a permanentelectric dipole moment (EDM) unless the discrete symmetries P and T are broken. Since then,measurements have been made on a variety of elementary particles, atoms and molecules, all with nullresults suggesting that T violation is not exhibited in ordinary matter. T violation does occur within thestandard model of elementary particle physics through complex Yukawa couplings between the quarks,indeed this mechanism accommodates the well-known CP-violating behaviour of kaons, but the EDMspredicted for ordinary matter are extremely small. This makes EDM measurements very powerful inthe search for new physics since any nonzero result immediately implies physics beyond the standardmodel. The present time is particularly exciting for this field because it is widely believed that thestandard model is incomplete and that new structure should exist in the energy range 100 GeV-10 TeV.Such new structure almost certainly means richer possibilities for T violation, including nonzeroelectric dipole moments in ordinary matter at a level that might be observable.

Sensitive measurements using molecules have the potential to give important information about thishigh-energy frontier of fundamental interactions. At Sussex, we have developed a new apparatus,based on the YbF molecule, which promises to measure the electron edm with unprecedentedsensitivity. It is easiest to think of our molecular beam experiment as an interferometer as illustrated infig. 1. Optical pumping first prepares the YbF molecules in the |F, mF> = |0,0> hyperfine state. Next,an adiabatic Raman transition is used to split the wavefunction into a coherent superposition of thestates |1,+1> and |1,-1> which are exactly degenerate, even in the presence of the applied electric field,as a consequence of time-reversal symmetry. These states have opposite electron spin and henceopposite dipoles ± de. As the superposition evolves in the electric field a phase difference ϕd = 2deffEefft/h builds up. A second Ramantransition going back to |0,0⟩recombines the two parts of thewavefunction, producing apopulation proportional to cos2 das in any interferometer.

We will report on the progress ofthe experiment and the current stateof calculations in YbF.

[1] P. G. H. Sandars, Phys. Rev. Lett. 19, 1396 (1967);O. P. Sushkov and V. V. Flambaum, Sov. Phys. JETP 48, 608 (1978); B. E. Sauer, JunWang, E. A. Hinds, Bull. Am. Phys. Soc. Ser. II 39, 1060 (1994);M. Kozlov and V. Ezhov, Phys. Rev. A 49, 4502 (1994).

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S11

Ab initio and DFT calculations on coinage metal containing systems

Jan Hrusák

Academy of Sciences of the Czech republic, J. Heyrovsky Institute of Physical Chemistry,Dolejskova 3, CZ-18223 Prague 8, Czech Republic

An overview about the recent work on cationic and some neutral copper, silverand gold complexes by means of different quantum chemical approaches is given. First,the individual methods are compared with each other and their reliability in predicting theexperimental structure and energy is carefully tested against the experimental data.

The cationic gold (I) complexes ( Au+(H2O), Au+(CO), Au+(NH3), Au+(C3H6),Au+(C6H6), and Au+(C2H4) ) and systems containing covalent and ionic bonds (Au-F,Au+=CH2, and Au+-CH3) have been examined by different ab initio and density functionalmethods using non-relativistic (NR) and relativistic ECPs and a quasi-relativisticapproach, where relativistic effects are explicitly taken into account. In general, therelativistic effects on structures and energetics of these gold(I) compounds are quite large.The interplay of electron correlation and relativistic effects is discussed.

On the one hand, Au+(H2O) and Au+(CO) exhibit binding energies (35.9 kcal/moland 44.1 kcal/mol, respectively, at theCCSD(T) level of theory) which arecomparable with those of the complexesof the group 11 congeners Cu+ and Ag+.While for Au+(NH3) and Au+(C2H4) alarge relativistic stabilization is observed,such that the binding energies (65.3kcal/mol and 68.8 kcal/mol, respectively,at the CCSD(T) level of theory) arealmost twice as high as for M+(NH3) andM+(C2H4) for M = Cu and Ag. The largestrelativistic stabilization is found for theAu+=CH2 where the bond dissociationenergy increase from 39.5 kcal/mol to94.2 kcal/mol if the relativistic effect istaken into account (Figure).

A discrepancy between the resultsof the "pure" DFT (BP) and the hybridmethod (B3LYP) is found. Contrary to MP2, CCSD(T), and B3LYP findings, and inagreement with the experiment, the BP calculated BDE of Au+(NH3) exceeds the bindingenergy of Au+(C2H4) by 4.7 kcal/mol. The predicted order of bond strengths is inexcellent agreement with gas phase ligand exchange reactions.

With respect to the computational methods applied, structural features andenergetics obtained with different ab initio (MP2, CCSD(T)) and DFT (ADF/BP andB3LYP) methods are in reasonable agreement with each other. The deviations in bondenergies between the CCSD(T) and B3LYP are smaller than 10 % for all three systemsstudied. Some comments are made on the difference between CCSD(T) and QCISD(T)methods and on the examples of CuF and CuH the failure of the QCISD approach isdocumented.

0

10

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40

50

60

70

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100

Cu Ag Au

M=CH2+

M-CH3+

Rel.

Rel.

N-Rel.

N-Rel.

CCSD(T)/ECP caculation

28

S12

Four-component relativistic coupled-cluster method

Uzi Kaldor

School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel

The Dirac-Coulomb-Breit Hamiltonian serves as a starting point for large-scale atomiccalculations. Correlation is included by the multireference Fock-space coupled-clustermethod at the singles-and-doubles level. The effective Hamiltonian approach employedyields a large number of states in one calculation. Spherical symmetry is used, withintegration over angular and spin coordinates done analytically by angular momentumalgebra. This allows for large basis sets, with l up to 8 programmed currently. A typicalbasis is 35s27p21d15f9g6h4i for Tl. Core polarization effects are included explicitly bycorrelating 15-40 electrons. Transition energies (ionization potentials, excitation energies,electron affinities) are calculated for many heavy atoms, with results usually within 0.1eV of experiment. The success of the method made possible predictions for the electronicstructure and spectra of superheavy elements, which often exhibit properties differentfrom those of lighter atoms in the same group.

New methodological developments will be discussed, in particular the application ofthe equation-of-motion method, which will make possible the study of inner-shell states.

29

S13

Relativistic Effects in Molecular Spectroscopy: Case Studies

Christel M. Marian

GMD National Research Center for Information TechnologyScientific Computing and Algorithms Institute (SCAI)

Schloß Birlinghoven, D-53754 Sankt Augustin, Germanyand

Institute of Physical and Theoretical ChemistryUniversity of Bonn

Wegelerstr. 12, D-53115 Bonn, Germany

The accurate quantum chemical prediction of spectroscopic properties of molecularsystems containing heavy atoms requires both electron correlation and relativistic effectsto be included in a calculation. A variety of methods have been devised which take theseinteractions into account - at different levels of approximation. Not unexpectedly the mostsophisticated approaches are also the most expensive ones in terms of computationalresources; they can therefore be applied to small molecules only. On the other hand, themore elaborate methods constitute a useful tool to gauge more approximate schemes. Inthis talk, I shall try to exemplify which methods can be used for a given size of moleculeand desired accuracy.As far as spin-orbit coupling is concerned, it turned out that transition and main groupelements put quite different demands on their theoretical treatment, and prototypes foreach class will be considered. Further, I shall briefly talk about compounds with lightconstituents such as carbohydrides; here, the percental contribution of two-electron termsto a spin-orbit matrix elememt is much larger - in the order of 50% - and it is thus notevident how well effective one-electron spin-orbit Hamiltonians will perform.In the discussion of the particular cases, I should like to concentrate on the followingpoints:

• four-component - two-component methods• jj-coupling - intermediate coupling - LS-type procedures• Breit / spin-other-orbit interaction• electron correlation• valence-only methods• effective spin-orbit Hamiltonians

30

S14

Vibrational and Electronic Structure of the Normal Auger Spectrum ofHBr Studied by Fully Relativistic Configuration Interaction

Calculations

T.Matila1, K.Ellingsen2, T.Saue3, H.Aksela1 and O.Gropen2

1Department of Physical Sciences, University of Oulu, Linnanmaa, FIN-90401 Oulu,Finland

2Institute of Mathematical and Physical Sciences, University of Tromsø, N-9037, Tromsø,Norway

3Laboratoire de Physique Quantique, IRSAMC, Université Paul Sabatier, 118 route deNarbonne, 31062 Toulouse Cedex 4, France

The recent development in the experimental techniques has made it possible to resolvenew spectral features in the Auger electron spectra (AES) of molecules. The large numberof close-lying electronic and vibrational states both in the intermediate and final state ofthe Auger process results in very complicated fine structures in the AES. Moleculescontaining one or more heavy element are cases were the assignment of these features,usually based on the assumption on the similarity of elements with similar outer shellstructure, easily fails.

Especially, for the core-hole states, the initial states of the Auger decay, there is an urgentneed to treat theoretically both the molecular field and spin-orbit interaction on the samefooting. The recent results by Ellingsen et al [2] indicated that relativisitic effects may beof importance in molecules as light as HCl when a highly excited states are involved. Inthe molecules as heavy as HBr the relativistic effects, especially the spin-orbit interaction,may be of importance also in the valence doubly-ionized states, the final states of theAuger decay. The relativistic molecular calculations are a natural choice for predictingthe properties of such states. It should be remembered that in the final states thecorrelation effects are of even more importance and the relativistic correlation treatmentby using methods like configuration interaction (CI) should be employed as well.

In this work we present results of fully relativistic calculations for the potential energycurves of the ground state and the 4pσ-2 ,4pσ-14pπ-1 and 4pπ-2 states of HBr2+. We alsoestimate the potential energy curves of the 3d-1 ionized, molecular-field-split, states ofHBr+. The potential energy curves obtained were used to describe the initial, intermediateand final states of the Auger transitions. The potential curves were further used forestimating the vibrational structure of the Auger spectra. It was found that the vibrationalbands are distorted due to lifetime vibrational interference.

The results of the calculations are directly compared to the experimental values obtainedby the Püttner et al [1]. The results are also compared to the calculations performed byBanichevich et al [3]. They described the major relativistic effect, spin-orbit interaction,as to cause predissociation in the non-relativistically stable states.

Fully relativic methods are shown to provide an effective tool to predict the energeticsand vibrational structures of the molecules containing heavy element(s). The accurary ofthe method compared to non-relativistic treatment should be tested with some heaviermolecule, e.g. HI, where the relativistic effects are expected to be even more pronouncedalso in the valence region.

[1] R. Püttner, Y.F.Hu, G.M.Bancroft, H.Aksela, E.Nõmmiste, J.Karvonen, A.Kivimäki,and S.Aksela, submitted to Phys.Rev.A.

[2] K. Ellingsen, T. Saue, H. Aksela, and O. Gropen, Phys. Rev. A 55, 2743 (1997)[3] A. Banichevich, S. D. Peyerimhoff, B. A. Hess, and M. C. van Hemert, Chem. Phys.

154, 199 (1991)

31

S15

An Experimentalist’s View of Relativistic Effects in Chemistry andSpecifically Aurophilicity

D. Michael P. Mingos

Chemistry DepartmentImperial College of Science Technology and MedicineSouth Kensington, London SW7 2AY, United Kingdom.

In common with the majority of the transition metals gold forms a wide range of metal-metal bonded and cluster compounds in its lower oxidation states. Gold-phosphinefragments, Au(PR3), also exhibit an almost unique ability to form hypervalent compoundswith the lighter main group elements. For example, [Au6C(PPh3)6]

2+ and [Au5N(PPh3)5]2+

prepared by Schmidbaur and his co-workers have carbon and nitrogen in unusual six andfive co-ordinate environments. Whether the ability of gold to from weak gold-gold bonds(aurophilicity) contributes significantly to these observations will be discussed.

In many gold(I) compounds the geometry around the metal is essentially linear,provoking the description that the metal is ds hybridised. In the crystalline state thesecompounds exhibit additional contacts to other gold atoms which are significantly longerthan the metal-metal distance in the metal itself ( 288.4pm) but shorter than that expectedfrom the sum of the estimated van der Waals radii of gold (360pm). These interactionsare analogous to weak hydrogen bonds and can have many interesting structural andchemical consequences. The energetics and origins of these interactions will be discussedand the structural consequences will be highlighted with examples from our ownexperimental results.

32

S17

Improved Configuration Interaction Techniques for the evaluation ofspin-orbit and spin-spin matrix elements and for theoretical analyses of

the fine structure of electronic levels and molecular properties.

Alexander O. Mitrushenkov

Department of Theoretical Physics, Institute of PhysicsSt. Petersburg University

198904 St. Petersburg, Russia

Maria Pilar De Lara Castells, Paolo Palmieri

Dipartimento di Chimica Fisica ed InorganicaUniversità di BolognaViale Risorgimento 440136 Bologna , Italy

The algorithm, recently developed for large full or nearly full Configuration InteractionExpansions of approximate molecular wavefunctions, has been improved for accuratepredictions of spin-orbit and spin-spin interactions and for theoretical analyses of the finestructure of electronic levels and molecular properties. In particular, to extend the rangeof applicability to more general types of problems in molecular physics and to exploit thepower of the algorithm, originally designed for benchmark computations on simplemolecules with very small basis sets, strategies have been investigated for the optimalselection of the CI orbitals to include all important correlation contributions and obtainmatrix elements very close to CI convergence.A few applications will be presented to test the accuracy of the method; in particular, thefine structure of ground and lowest excited electronic states of Si2

- and of the 4Πg

autoionizing excited electronic state of He2-.

A detailed time dependent treatment of predissociation of OH in the lowest excited state,including all fine structure interactions, is on progress and, hopefully, preliminary resultswill be presented at the conference.

33

S18

Atoms through the looking glass

Ann-Marie Mårtensson-Pendrill

Göteborg, Sweden.

Experimental studies of parity non-conservation in heavy atoms have emphasized theneed for reliable relativistic many-body calculations and stimulated the development ofsuch methods, involving both computational and formal aspects. The increasedexperimental accuracy points to a need for a better understanding of details in the nuclearstructure. Since the parity non-conserving interactions take place within or close to thenucleus, a good description of the electronic wavefunction is essential, requiringknowledge of the charge distribution. In addition, experiments for isotope chains aresensitive to isotopic variations in the neutron distribution. Experiments searching for anatomic electric dipole moment (EDM) probe the distribution of nuclear EDM, as well asother P and T violating effects. By combining experimental and theoretical results foratomic isotope shifts and hyperfine structure anomalies, information about nuclear chargeand magnetization radii can be extracted, thereby providing additional calibration fornuclear theory.

34

S19

Relativistic quantum chemistry: recent results.

Pekka Pyykkö

The recent activity in the author's group includes:

1) New results in the chemistry of gold, both on the aurophilic attraction and on newspecies.

2) Studies on the metallophilic attraction in In(I) and Tl(I) compounds (see also the posterby M. Straka).

3) Estimates for the effects of the Lamb shift for heavy alkali and coinage metal atoms.The QED appears to contribute about -1 per cent of the kinetic, Dirac-level effects forlarge Z, and up to -8 per cent of them for Li. The effects on electronic g-factors are undercurrent study.

4) NMR parameters.

35

S20

Ab initio four-component relativistic electronic structure calculationsusing BERTHA.

Harry M. Quiney

School of Chemistry, University of Melbourne, Parkville, Victoria 3052, AUSTRALIA

This presentation will outline the methods and strategies which have been incorporated inBERTHA, an ab initio four-component relativistic electronic structure program, whichwas developed in Oxford by Quiney, Skaane and Grant. This is part of our continuingstudies of relativistic and quantum electrodynamic effects in heavy-element chemistryand physics.Our general approach is built around explicit representations of the charge and currentdensities generated by two-component G-spinor basis functions, satisfying strictly thekinetic balance condition. Two-electron integrals involving the Coulomb and Breitinteractions, matrix representations of the one-electron Dirac operator, and integralsencountered in the evaluation of electric and magnetic properties, are readily incorporatedwithin our adaption of the McMurchie-Davidson algorithm. Electron correlation effectshave been incorporated using a direct implementation of second-order many-bodyperturbation theory.The utility of our approach will be illustrated using a selection of all-electron calculationsof relativistic electronic structures. These will include a study of relativistic, many-body,NMR, and Breit interaction effects in the water molecule, and of hyperfine, many-body,and PT-odd interactions in the open-shell diatomic radical, YbF.Prospects for further development will be discussed including adapting our computationalmethods to four-component density functional calculations.

36

S21

The Symmetric Group Approach to Spin-Dependent Properties

Sten Rettrup

Department of Chemistry, Copenhagen University,Universitetsparken 5, DK-2100 Copenhagen Ø , Denmark

The symmetric group approach to the many-electron correlation problem is one of thepossible methods for handling electron correlations in the framework of spin-freequantum chemistry. The same approach and algorithms, however, may also be applied inmany-electron problems involving spin-dependent properties and operators.In the present talk, particular emphasis will be put on the evaluation of the requiredmatrix elements between Configuration State Functions (CFS's) over spin-dependentoperators. It will be demonstrated how they may be obtained extremely symply byhandling the space and spin variables separately.For computational applications recently developed methods and graphical techniques forevaluating the associated coupling-coefficients and corresponding irreducible matrixrepresentations of the symmetric group, SN, will be discussed.

References:The presented work is a result of collaborations with:Prof. C.R. Sarma,Ph.D. student T. la Cour Jansen,Prof. P. Palmieri,Prof. J.G. Snijders,Prof. R. Paunczand Ph.D. student B. Friis-Jensen.

37

S22

Structural Properties of M(dmit)2(M = Ni, Pd, Pt, dmit2- = 2-Thioxo-1,3-dithiole-4,5-dithiolato) Based Molecular Metals. Insights from

Relativistic Density Functional Calculations

Angela Rosa,a Giampaolo Ricciardi,a Evert Jan Baerendsb

a Dipartimento di Chimica, Università della Basilicata, Via N. Sauro, 85, 85100 Potenza,Italy

b Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands

The bonding between two M(dmit)2 monomers (M=Ni, Pd, Pt) in the stacks that arecharacteristic for the crystal structure of these compounds has been analyzed, usingdecomposition of the interaction energy in steric repulsion, electron pair bond and donor-acceptor interactions. Atom over atom (eclipsed) stacking may occur if two conditions aremet: (a) The HOMO to LUMO excitation energy should be small enough so that thesesingly occupied orbitals may both form an electron pair bond with their partner on theadjacent monomer. The HOMO and LUMO both being ligand based, the electron pairbonds are between the ligands, not between the metals. (b) The bending away of theligand systems so as to relieve the steric hindrance should not cost too much energy.These circumstances prevail in Pt(dmit)2, where relativistic effects increase the stabilityof the eclipsed conformation by enhancing the acceptor capability of the virtual orbitalswith 6s, 7s and 6pz character on the metal for electron donation out of the occupiedadjacent dz2. In Ni(dmit)2 both the excitation energy is somewhat higher and the bendingis more unfavourable, consequently this does not exhibit the eclipsed stacking pattern.Slipping is another way to relieve the steric repulsion between adjacent monomers. Theelectron pair bonds are broken in that case, but sufficient donor-acceptor interactionsbetween the two ligand systems remain to make this a viable alternative for Ni(dmit)2.Pd(dmit)2 is in between and may adopt either eclipsed or slipped configurations.

38

S23

Gold Chemistry: From Alchemy to Relativity and Back

Hubert Schmidbaur

Lehrstuhl fur Anorganische und Analytische ChemieTechnische Universität München

Lichtenbergstraße 4, D-85747 Garching

Although gold chemistry arose from the alchemy of the 15th-18th centuries, the subjectremained undeveloped for many years. The recent dramatic expansion of research in goldchemistry has been stimulated by the emergence of several technologically importantapplications. Gold and its compounds have also excited the interest of theoreticalphysicists and chemists because the element serves as a unique reference point for thestudy of relativistic and correlation effects. Many phenomena in gold chemistry can beinterpreted on the basis of such effects but others remain puzzling and poorly unterstood .Current mainstream gold research is directed mainly towards the structural aspects ofsupramolecular frameworks and nanotechnology. The aggregation of gold complexesthrough various types of secondary bonding leads to unprecedented self-assemblypatterns with interesting consequences for structure and associated photophysicalpropertics. While some of these can be rationalized, others have the character ofalchemistic mysteries, mainly owing to a delicate balance of various small effectscontributing to the equilibria of a given system.

39

S24

Chemical Bonding and the Hellmann-Feynman Theorem in RelativisticQuantum Chemistry

W.H.Eugen Schwarz*, Jochen Autschbach and Andrzej Rutkowski

Theoretische Chemie, Universität, D-57068 [email protected]

Relativity changes the structure (e.g. bond lengths), energetics (bond energies) anddynamics (e.g. force constants) of molecules. Relativity originates near the nuclei, whilebonding is thought to originate in the outer atomic valence shells. Explanations ofrelativistic effects in chemistry are, therefore, sometimes somewhat involved andparadoxical. In addition, one may focus on energetic or on force aspects; one may use 4-component or 2-component approaches; one may apply all-electron or frozen core orpseudopotential valence-only approaches; one may use zero or first order wavefunctions;one may change the gauge of the forces. Combining different viewpoints yields a deeperunderstanding of relativistic quantum chemistry [1].An important tool in this research is direct relativistic perturbation theory (DPT),extended to the case of near-degenerate states [2,3]. In addition, the force theorem ofHellmann and Feynman has been applied to the relativistic case. News about the origin ofthis theorem and about the live and fate of Hellmann will also be reported [4].

References

[1] J. Autschbach, W.H.E. Schwarz: Relativistic Corrections to Chemical Forces; J.Autschbach, M. Seth, P. Schwerdtfeger, W.H.E. Schwarz: Trends and Extrema ofRelativistic Effects of Atomic Oribitals; in preparation

[2] A. Rutkowski, W.H.E. Schwarz, R. Kozlowski, J. Beczek, R. Franke, J. Chem. Phys.109 (1998) 2135

[3] W. Kutzelnigg, in press[4] W.H.E. Schwarz et al., Bunsenmagazin 1(1) (Jan. 1999) 10-21; 1(2) (March 1999), in

press

40

S25

QED effects in high-Z few-electron atoms

Vladimir Shabaev

St.Petersburg State University, Russia

The present status of the quantum electrodynamic theory of high-Z few-electron atoms isreviewed. The currently available theoretical results for the Lamb shift, the hyperfinestructure splitting, and the bound-electron g-factor in heavy few-electron atoms arecompared with recent experiments. A special attention is focused on testing the quantumelectrodynamics in regions which were not available before.

41

S27

GRECP method and procedures of electronic structure restoration incores of heavy-atom systems

Anatoli V. Titov and N. S. Mosyagin

St.-Petersburg Nuclear Physics Institute, St.-Petersburg, RUSSIA

The shape-consistent Relativistic Effective Core Potential (RECP) approximation to the Dirac-Coulomb (DC) method is successfully applied to numerous calculations of spectroscopic and otherphysical and chemical properties of heavy-atom molecules. In the RECP method only valence andsome outer-core shells are treated explicitly, the shapes of spinors are smoothed in the atomic coreregions and the small components of four-component spinors are excluded from calculations.Therefore, the computational efforts can be dramatically reduced.It is clear that the inclusion of the outer-core electrons into the space of explicitly treated electrons isthe way to increase an accuracy of the calculations and to extend the field of applications. However,in the framework of the standard radially-local RECP versions, any attempt to extend this spacemore than some limit does not improve the accuracy of the calculations. The errors caused by thenodeless RECPs can range up to 2000 cm-1 and more for the dissociation and transition energieseven for lowest-lying excitations that can be unsatisfactory for many applications.Moreover, the direct calculation of such properties as electronic densities near heavy nuclei,hyperfine structure, and matrix elements of other operators singular on heavy nuclei is impossible asa result of the smoothing of the orbitals in the core regions.In the present talk, ways to overcome these disadvantages of the RECP method are discussed.It is shown that the difference between the valence and outer-core effective potentials with the sameangular and total electronic momenta should be taken into account in precise RECP calculations, andthe corresponding Generalized RECP (GRECP) operator including nonlocal terms with theprojectors on the outer-core pseudospinors in addition to the semilocal RECP operator is suggested.These terms are important for the accurate simulation of interactions with the valence electrons.Additional terms in the RECP operator correcting the interaction of the explicitly treated outermostd,f-electrons with the inner core electrons (excluded from the RECP calculations) in transitionmetals, lanthanides, and actinides together with the spin-orbit correction and other improvements arealso discussed. The possibility to take into account correlations with the inner core electrons withinthe GRECP method is considered.For the evaluation of the matrix elements of operators that are singular near a heavy nucleus, theproper shapes of the valence molecular orbitals must be restored in the atomic core region after themolecular RECP calculation with the smoothed pseudoorbitals. Both non-variational and variationalrestoration procedures are developed. The promising destination of these procedures is a "splitting"of the correlation structure calculation of a molecule into two sequential steps: the calculation in thevalence region and the subsequent restoration in the core regions. The basic principles of therestoration techniques are discussed.The suggested developments of the RECP method are studied in many test calculations. Thenonvariational restoration technique is applied to calculation of the P,T-odd spin-rotationalHamiltonian parameters including the weak interaction terms which break the symmetry over thespace inversion (P) and time-reversal invariance (T) in the YbF, BaF and other molecules.

42

S28

Density functional calculations of molecular properties in the zero orderregular approximation for relativistic effects

Erik van Lenthe

Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam,De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands

The zeroth order regular approximated (ZORA) relativistic equation, available in theAmsterdam Density Functional program, has recently been used in the calculations ofESR parameters (g-tensor [1], hyperfine interaction tensor [2]) of Kramers doublet openshell molecules.The ZORA method has now been applied for density functional calculations of theelectric field gradients (EFG), with the use of numerical integration, at the position of thenuclei in several molecules. Relativistic effects on the calculated nuclear quadrupolecoupling constants (NQCC) were investigated. As was pointed out by before the effectsof picture change can be important.

[1] E. van Lenthe, P.E.S. Wormer, and Ad van der Avoird, J. Chem. Phys. 107 (1997)2488.

[2] E. van Lenthe, A. van der Avoird, and P.E.S. Wormer, J. Chem. Phys. 108 (1998)4783.

43

S29

The ZORA approach in Ab Initio Quantumchemistry

Joop H. van Lenthe

Theoretical Chemistry GroupDebye Institute

Utrecht UniversityPadualaan 14

3584 CH UtrechtThe Netherlands

The Zeroth Order Regular Approximation (ZORA) transforms the Dirac Hamiltonian intoa two-component form. The method, originally proposed by Chang et al.[1] and Heully etal.[2] for atomic systems, was first applied to molecules in a density functional formalismby van Lenthe et al.[3]. It gives a two-component relativistic Hamiltonian that isvariationally stable. The neglect of spin-orbit coupling yields scalar ZORA, which is aone-component real formalism. We present an implementation of the formalism in an AbInitio framework.The scalar ZORA allows, in principle, any non-relativistic quantumchemistry techniqueto be employed, including the major part of the relativistic effect. We describe aspects ofthe implementation in (MC)SCF and CI and related technique within theQuantumchemical program GAMESS-UK{4] and discuss ways to extend the formalismto include e.g. gradients and approximate inclusion of spin-orbit effects. The full ZORAHamiltonian, allowing variational inclusion of spin-orbit effects, has been implementedwithin the Hartree-Fock framework.We demonstrate the accuracy of both ZORA and basis-set approximations for atoms bycomparison with numerical ZORA and Dirac-Fock results. Molecular calculations will bepresented for transition metal complexes and noble-gas dimers.This research is a collaboration between the Theoretical Chemistry Group, UtrechtUniversity (S. Faas and J.H. van Lenthe) and the Theoretical Chemistry Group,University of Groningen (J.G. Snijders)

[1] Ch. Chang, M. Pellisier & Ph. Durand, Phys. Scripta 34, 394 (1986)[2] J.-L. Heully, I. Lindgren, E.Lindroth, S. Lundquist & A.M. Martensson-Pendrill, J.

Phys. B. 19, 2799 (1986)[3] E. van Lenthe, E.J. Baerends, J.G. Snijders, J. Chem. Phys. 99, 4597 (1993)[4] M.F. Guest, J.H. van Lenthe, J. Kendrick, K. Schoeffel, P. Sherwood & R.J. Harrison,

GAMESS-UK, CFS Ltd, (Daresbury, 1998)

44

S30

Relativistic calculations on actinyl complexes

Ulf Wahlgren

Institute of Physics, Stockholm UniversityBox 6730, S-113 86 Stockholm, Sweden

The actinides are difficult from a theoretical point of view both because of the relativisticeffects and the role of the 5f-orbitals.In the present contribution we have investigated the reduction of actinyl(VI) for U to Amusing different methods. We have also studied the dissociation of dioxo-uranium andcompared our results with experiment. Finally, we will describe results obtained foruranyl(VI) in solution. In general, our results agree well with experiment.

45

Poster presentersalphabetic order, with abstract number

P01 S. A. Alexander, R.L. Coldwell, Edinburg, USA, [email protected] Calculations using Monte Carlo Methods

P02 D. Andrae, M. Reiher, J. Hinze, Bielefeld, Germany, [email protected] comparative study of finite nucleus models for low-lying states of few-electron high-Zatoms

P03 Rodolfo H. Romero and Gustavo A. Aucar, Corrientes, Argentina,[email protected] theory for magnetic response properties in molecules

P04 Jacek Bieron, Per Jönsson, Charlotte Froese Fischer, Ian P. Grant, Krakow, Poland,[email protected] MCDF calculations of atomic hyperfine structures

P06 P. Indelicato, E. Lindroth, S. Boucard, Paris, France, [email protected] non-relativistic limit in the Multiconfiguration Dirac-Fock method

P09 E. Charro and I. Martín, Valladolid, Spain, [email protected] effects in spectral properties of atomic systems. RQDO and MCDFcalculations

P10 W. A. de Jong, R. J. Harrison, H. H. Cho, Richland, USA, [email protected] Relativistic Calculations on Uranyl Compounds as Benchmark for Theory andSupport for Experiment

P11 W. A. de Jong, Richland, USA, [email protected] "Computational Chemistry for Nuclear Waste Characterization and Processing:Relativistic Quantum Chemistry of Actinides" Program

P12 Maria Pilar de Lara Castells, Alexander O. Mitrushenkov and Paolo Palmieri,Bologna, Italy, [email protected] tecniques for spin-dependent properties: a theoretical analysis of predissociation ofOH in its lowest excited state

P13 Ephraim Eliav and Uzi Kaldor, Tel Aviv , Israel, [email protected] Multireference Relativistic 4-Component Coupled Cluster Methods: Some recentprogress

P14 Timo Fleig, Jeppe Olsen, Christel M. Marian, Bonn, Germany, [email protected] Generalized Active Space (GAS) configuration interaction concept in two-component relativistic theory

P16 Laura Gagliardi, Nicholas C. Handy, Andrew G. Ioannou, Chris-Kriton Skylaris,Steven Spencer, Andrew Willetts, Adrian M. Simper, Bologna, Italy,[email protected] Density Functional Calculations on Large Molecules Containing Actinides

46

P17 M. R. Godefroid and Charlotte Froese Fischer, Brussel, Belgium, [email protected] calculations of transition rates of astrophysical interest in neutral Technetium.

P18 Harry Quiney and Ian Grant, Oxford , UK, [email protected] methods for four-component molecular calculations

P20 Elsa S. Henriques, Margarida Bastos, Carlos F. G. C. Geraldes and M. Joao Ramos,Porto, Portugal, [email protected] study of some lanthanide (III)-polyazamacrocyclic chelates for magneticresonance imaging

P21 L. de Billy, S. Boucard and P. Indelicato, Paris, France, [email protected] Dirac-Fock calculation of 1s2p 1P1 and 1s2p 3P1 levels in the high Zhelium-like ions

P22 P. Norman and H. J. Aa. Jensen, Odense, Denmark, [email protected] Dirac-Hartree-Fock response

P24 Mika Kivilompolo, Reinhold F. Fink, Helena Aksela, and Seppo Aksela, Oulu,Finland, [email protected] initio calculation of the molecular field and spin orbit split components of L2,3VVAuger spectra

P28 Thomas la Cour Jansen, S.Rettrup, J.G.Snijders, P.Palmieri, C.R.Sarma,Groningen, The Netherlands, [email protected] of Spin-orbit coupling constants using the Symmetric Group Approach ofConfiguration Interaction

P29 Arik Landau, Tel Aviv, Israel, [email protected] Coupled-Cluster Approach

P30 Yoon Sup Lee, Taejon, Korea, [email protected] spin-orbit calculations for the molecules containing heavy orsuperheavy atoms

P31 Wenjian Liu, Bochum, Germany, [email protected] MCSCF by means of direct perturbation theory : theory and implementation

P32 Carlo Adamo and Pascale Maldivi, Grenoble, France, [email protected] structure of complexes containing f elements : a DFT study including scalarrelativistic effects.

P33 G. Malli, J. Styszynski, E. Eliav, U. Kaldor and L. Visscher, Burnaby, BC, Canada,[email protected] Fock Space Coupled-Cluster Calculations for Molecules with HeavyElements: ThF4 and AuH

P34 Valérie Vallet, Laurent Maron, Thierry Leininger, Christian Teichteil, BerndSchimmelpfennig, Ulf Wahlgren, Toulouse, France, [email protected] thermodynamics of actinide oxides

P35 T. Marrel, Ch.Daussy, M. Ziskind, Ch.J. Bordé and Ch. Chardonnet, Paris, France,[email protected] precision test of parity violation in the spectrum of the chiral molecule CHFClBr

47

P37 Spiridoula Matsika and Russell M. Pitzer, Ohio, USA, [email protected] initio calculations of the NpO2

2+ and NpO2+ ions.

P38 Markus Mayer, Notker Rösch, München, Germany, [email protected] Self-Consistent Two-Component Density Functional Implementation of Spin-OrbitCoupling within the Douglas-Kroll-Hess Scheme.

P39 Jan Micanko and Stanislav Biskupic, Bratislava, Slovak Republic,[email protected] Gaussian basis sets and molecular relativistic calculations

P42 Grzegorz Pestka, Torun, Poland, [email protected] exact Dirac-Coulomb ground state energies of helium-like ions

P43 Ian Grant and Harry Quiney, Melbourne, Australia, [email protected] quantum chemical approach to QED

P44 C. Rabbe, J.P. Dognon, Bagnols-sur-Ceze, France, [email protected] Calculations With Effective Core Potentials On Terpyridine-Ln(III)Complexes.

P45 Sophie Hoyau, Valérie Brenner, Jean-Pierre Dognon, Philippe Millié, Marcoule,France, [email protected] (presented by C. Rabbe)The charge transfer in small ion-molecule systems : calculation and modeling.

P46 Markus Reiher, Juergen Hinze, and Dirk Andrae, Bielefeld, Germany,[email protected] frequency-independent Breit interaction in relativistic atomic structure calculations

P47 G. Rodrigues, P. Indelicato, E. Lindroth, Paris, France, [email protected] binding energies of Cs ions. A comparison between Multiconfiguration Dirac-Fockand Relativistic Many Body Perturbation Theory correlation energies.

P48 Norbert Roehrl, Regensburg, Germany, [email protected] energy of the relativistic electron-positron field

P49 Nino Runeberg, Martin Schütz and Hans-Joachim Werner, Helsinki, Finland,[email protected] aurophilic attraction as interpreted by local correlation methods

P50 B. Schimmelpfennig, L. Maron, V. Vallet, Th. Leininger, O. Gropen and U.Wahlgren, Stuttgart, Germany, [email protected] the redox behaviour of actinide compounds in gas phase and solution

P51 Luis Seijo, Madrid, Spain, [email protected] ab initio model potential relativistic treatment of Ce and CeO.

P52 Pekka Pyykkö, Michal Straka, Helsinki, Finland, [email protected] interactions in the systems [MH]2 and [M(C5H5)]2, M=In, Tl

P55 James D. Talman, London, Ont. Canada, [email protected] integral calculations for numerically defined orbitals

48

P56 J. Thyssen and H. J. Aa. Jensen, Odense, Denmark, [email protected] geometry optimization

P57 Valérie Vallet, Laurent Maron, Christian Teichteil, Jean-Pierre Flament, Toulouse,France, [email protected] effective Spin-orbit - CI treatment

P58 Christoph van Wüllen, Bochum, Germany, [email protected] quasirelativistic CPD operator in molecular calculations.

P59 Lucas Visscher and Erik van Lenthe, Amsterdam, The Netherlands,[email protected] distinction between scalar and spin-orbit relativistic effects.

P60 V. A. Yerokhin, A. N. Artemyev, T. Beier, G. Plunien, V. M. Shabaev and G. Soff,St.Petersburg, Russia, [email protected] self-energy and vacuum-polarization corrections to the 2p1/2 -2s transition oflithium-like ions

49

Poster Abstracts

50

P01

Relativistic Calculations using Monte Carlo Methods

S.A. Alexander

Department of Physics and GeologyUniversity of Texas Pan American

Edinburg, TX 78539

R.L. Coldwell

Department of PhysicsUniversity of Florida

Gainesville, FL 32611

Variance minimization and Monte Carlo integration are used to evaluate the 4-component Dirac equation for a number of one-electron atomic and diatomic systems.This combination produces accurate energies, is relatively simple to implement andexhibits few of theproblems associated with traditional techniques. We also examine whatis needed to extend this approach to the helium atom and to even larger systems.

51

P02

A comparative study of finite nucleus models for low-lying states of few-electron high-Z atoms

D. Andrae, M. Reiher, J. Hinze

Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld,Postfach 10 01 31, D-33501 Bielefeld, Germanyf

The use of extended models instead of the point-like nuclear charge density distributionto represent atomic nuclei is known not only to have technical advantages in relativisticelectronic structure calculations for atoms or molecules. Such nuclear models alsoprovide advantages in the accurate calculation of various physical properties probing thedistribution of electrons close to the nucleus. Some `popular' nuclear models have beenused in a recent numerical Dirac-Hartree-Fock study of electronic states of neutral atomsby Visscher and Dyall [1], demonstrating a marginal influence of the various nuclearmodels (standardized to a common rms radius) on the total energies of neutral atoms. Thesituation is different for energy differences and total energies of low-lying states ofhydrogen-like high-Z atoms, as has been shown by one of the authors [2]. An extensionof the latter work to low-lying states of few-electron high-Z atoms will be presented.

f E-mail: [email protected], [email protected], [email protected]

[1] L. Visscher, K. G. Dyall, At. Data Nucl. Data Tables 67 (1997) 207-224.[2] D. Andrae, Finite nuclear charge density distributions in electronic structure

calculations for atoms and molecules (review), submitted for publication (1998).

52

P03

QED theory for magnetic response properties in molecules

Rodolfo H. Romero and Gustavo A. Aucar

Facultad de Ciencias Exactas y Naturales y Agrimensura. Universidad Nacional delNordeste. Avda. Libertad 5300 (3400) Corrientes, Argentina

E-mail address: [email protected], [email protected]

The current way to include relativistic effects on calculations of magnetic molecularproperties are separated in scalar, 2-component or 4-component (full relativistic) basedformalism. All of them starts from Dirac, Pauli or Schrödinger schemes and useperturbation theory (or response theory) to include the correction to the energy which isrelated with the property analyzed. In this communication we present a new formalismwhich treat quantized magnetic field and second quantized boson and fermion operators;this is done, to our knowledge for the first time. We use perturbation theory applied alsoon operators. The fine structure constant is used as perturbative parameter. Thisformalism is applied on NMR-J tensor calculations. We obtain the different contributionsto J, i.e., the usual direct and indirect nuclear spin couplings when magnetic fields areassumed as classical. We also get the QED contributions in a natural manner. Relativisticcorrections arise when their 4-component implementation is reduced by current methodsto two- or one-component expressions.

53

P04

Large-scale MCDF calculations of atomic hyperfine structures

Jacek BieronInstytut Fizyki, Uniwersytet Jagiellonski, Reymonta 4, 30-059 Kraków, Poland

email: [email protected]

Per JönssonDepartment of Physics, Lund Institute of Technology, S-221 00 Lund, Sweden

Charlotte Froese FischerComputer Science Department, Vanderbilt University, Nashville, TN 37235, USA

Ian P GrantMathematical Institute, University of Oxford, Oxford OX1 3LB, UK

The goal of this study is to investigate systematically the computation of atomic hyperfinestructures within the framework of the multiconfiguration Dirac-Fock (MCDF) model.We have employed an MCDF code, which has been developed at Vanderbilt Universityover the last couple of years[1]. It has been derived from Oxford GRASP[2] package,modularized, and designed to handle expansions of several thousand Configuration StateFunctions. To facilitate large-scale calculations the code implements dynamic memoryallocation, new methods for solving differential equations[3], and an eigenvalue solver,which uses a sparse representation of the lower triangular part of the Hamiltonianmatrix[4]. The package in its present form makes it possible to study the convergence ofatomic properties when the configuration expansion is increased in a systematic way.The configuration expansions were obtained with the active space method in whichconfiguration state functions of a particular parity and symmetry are generated bysubstitutions from reference configuration to an active set of orbitals. The active set isthen increased systematically until the convergence of the hyperfine constant is obtained.Several schemes were studied, where certain limitations are employed to keep the numberof configuration state functions below the limit acceptable by the computer memoryconstraints.Calculations of the hyperfine parameters were chosen as test cases. The calculatedmagnetic dipole hyperfine structure constants of several low-lying states of neutralLithium, Lithium-like Beryllium and the ground state of Lithium-like Fluorine will becompared with experiment and with values obtained by other theoretical methods. As anapplication to heavy systems, we have chosen the calculations of the electric quadrupolehyperfine constants of several states of Scandium, Yttrium, and Titanium ions. Thecomparison of the calculated hyperfine constants with experimentally determinedhyperfine energy splittings yields the values of nuclear electromagnetic moments.

References

[1] F. A. Parpia, C. Froese Fischer, I. P. Grant, Comput. Phys. Commun. (1996)[2] K. G. Dyall, I. P. Grant, C. T. Johnson, F. A. Parpia, E. P. Plummer, Comput. Phys.

Commun. 55, 425 (1989).[3] C. Froese Fischer, Comput. Phys. Rep. 3, 273 (1986).[4] A. Stathopoulos, C. Froese Fischer, Comput. Phys. Commun. 79, 1 (1994).

54

P06

The non-relativistic limit in the Multiconfiguration Dirac-Fock method

P. Indelicato, E. Lindroth, S. Boucard

Laboratoire Kastler-Brossel, Case 74, Universiti P & M Curie, 4 place Jussieu, F-75252Paris CEDEX 05 France

Many years ago it was pointed [1] that the Multiconfiguration Dirac-Fock method wasgiving incorrect results in the non-relativistic limit when there were several jjconfigurations originating from a single LS one. This effect is particularly striking in F-like ions where the 1s2 2s 2 2p5 J=3/2 and J=1/2 do not have the same energy in the nonrelativistic limit. Since then this problem was identified in correlation energy of threeelectron ions[2] and in spin-forbidden E1 transition probabilities [3]. A new explanationfor this problem is presented, with the help of many-body perturbation theory. We use F-like as a model to show how relaxation plays a major role in this problem

This work is partly funded by the EUROTRAP TMR network.

[1] K.N. Huang, Y.-K. Kim, K.T. Cheng and J.P. Desclaux, Phys. Rev. Lett. 48, 1245(1982).

[2] P. Indelicato and J.P. Desclaux, Phys. Rev. A. 42, 5139 (1990).[3] Y.K. Kim, F. Parente, J. Marques, P. Indelicato and J.P. Desclaux, Phys. Rev. A. 58,

R1885 (1998).

55

P09

Relativistic effects in spectral properties of atomic systems.RQDO and MCDF calculations.

E. Charro and I. Martín

Departamento de Química Física, Universidad de Valladolid,47011 Valladolid, Spain

Quantum-defect theories have been, over the years, generalised and applied to describecomplex atomic spectra, electron scattering, photoionisation, electron capture, and otherrelated properties. The Relativistic Quantum Defect Orbital (RQDO) method wasoriginally proposed by Martin and Karwowski (1991) and Karwowski and Martin (1991).It includes a mayor part of the relativistic effects at the same time its analytical natureallows one to formulate transition integrals as closed-form expressions. ThE calculationsof transition probabilities in atoms and molecules are, thus, free from convergenceproblems and numerical errors.We give a summary of the method and include several numerical examples of oscillatorstrengths that are relevant in astrophysics and plasma fusion research obtained with ourRQDO codes for medium- and high-Z atomic systemS, with and without explicitinclusion of core-polarization effects. In addition, we also show the values obtained by uswith the Multiconfiogurational-Dirac-Fock (MCDF) method, as implemented in theGRASP code (Dyall et al. 1989).Regularities in the oscillator strength for a given transition along an isoelectronicsequence of ions are also illustrated in graph form.

Karwowski J., Martín I., 1991 Phys. Rev. A43, 4832Martín I., Karwowski J., 1991 J. Phys. B: At. Mol. Opt. Phys. 24, 1538;Dyall K.G., GrantT I.P., Johnson C.T., Parpia F.A. and Plummmer E.P., 1989 Comput.Phys. Commun. 55, 425

56

P10

Fully Relativistic Calculations on Uranyl Compounds as Benchmark forTheory and Support for Experiment.

W. A. de Jong, R. J. Harrison, H. H. Cho.

Pacific Northwest National Laboratory, Environmental Molecular Sciences Laboratory,Mail stop K1-83, P.O. Box 999, Richland, WA, 99352.

Results of fully relativistic correlated benchmark calculations, using the MOLFDIRprogram package, on the uranyl ion will be presented and the results will be comparedwith those obtained from approximate methods. The electric field gradients at theuranium nucleus and oxygen nuclei in uranyl carbonate complexes are calculated and theresults are used as a guideline for NMR experiments on uranyl compounds. Future plansfor calculations on NMR properties and the interaction between theory and experimentwill be outlined.

This work was supported by the U.S. Department of Energy, MICS / OCTR undercontract DE-AC06-76RLO 1830 with Battelle Memorial Institute (Pacific NorthwestNational Laboratory).

57

P11

The “Computational Chemistry for Nuclear Waste Characterizationand Processing: Relativistic Quantum Chemistry of Actinides”

Program.

W. A. de Jong

Pacific Northwest National Laboratory, Environmental Molecular Sciences Laboratory,Mail stop K1-83, P.O. Box 999, Richland, WA, 99352.

The production of nuclear weapons at Department of Energy (DOE) facilities has left aserious legacy of environmental contamination, including millions of gallons of highlyradioactive waste stored in hundreds of tanks which have exceeded their life expectancy.Much of the radioactive waste involves actinides, and their large atomic number impliesthat relativistic effects have important chemical consequences.The “Computational Chemistry for Nuclear Waste Characterization and Processing:Relativistic Quantum Chemistry of Actinides” program aims to develop and apply themethods of relativistic quantum chemistry to assist in the understanding and prediction ofthe chemistry of actinide and lanthanide compounds. The theoretical and computationalmethodology so developed will supplement current, very expensive experimental studiesof the actinides and lanthanides. This will allow limited experimental data to beextrapolated to many other regimes of interest. The program objectives will be attainedthrough a multi-laboratory, multi-university and multi-disciplinary collaboration. Thesetechniques will be applied to important molecular systems and processes, including theinteraction of actinides with: 1) organic complexing agents present in tank wastes; 2)natural aqueous systems (carbonates), in order to better understand fate and transport inthe environment; and 3) new materials, such as phosphates and amides, for the design ofin situ remediation technologies and separation systems. The systems to be studied willbe chosen to aid on-going experimental and theoretical efforts at Pacific NorthwestNational Laboratory (PNNL) and other sites, and to have maximum impact on solvingDOE's environmental remediation problems.On this poster we will give an overview of the program, it’s current research projects andcollaborators.

More information can be found http://www.emsl.pnl.gov:2080/proj/tms/hpcc-actinides

This work was supported by the U.S. Department of Energy, MICS / OCTR undercontract DE-AC06-76RLO 1830 with Battelle Memorial Institute (Pacific NorthwestNational Laboratory).

58

P12

CI tecniques for spin-dependent properties: a theoretical analysis ofpredissociation of OH in its lowest excited state

Maria Pilar De Lara Castells, Paolo Palmieri

Dipartimento di Chimica Fisica ed InorganicaUniversità di BolognaViale Risorgimento 440136 Bologna , Italy

Alexander O. Mitrushenkov

Department of Theoretical Physics, Institute of PhysicsSt. Petersburg University

198904 St. Petersburg, Russia

The state specific predissociation of OH in its lowest excited state (A 2Σ+, v', N', F1/F2) isinvestigated using time dependent wave propagation tecniques. All required potentialenergy curves, spin-orbit, spin-spin and rotation interactions have been obtained byimproved CI tecniques1. A detailed description of the CI methods will be presented. Thematrix elements, the potential energy curves and the lifetimes of the rotational sublevelsof OH will be compared to experiment and to values from multichannel scatteringtheory3.

References.

[1] Alexander O. Mitrushenkov and P. Palmieri, Molecular Physics, 1997, Vol. 92, No. 3,511-522.

[2] Gerard Parlant and David R. Yarkony, Journal of Chemical Physics, 1999, Vol. 110,No. 1, 363; D. R. Yarkony, J. Chem. Phys, Vol. 97, 1838 (1992).

[3] J. J. L. Spaanjaars, J. J. ter Meulen, and G. Meijer, J. Chem. Phys. Vol. 107, 2242(1997).

59

P13

The Multireference Relativistic 4-Component Coupled ClusterMethods: Some recent progress

Ephraim Eliav and Uzi Kaldor


Different high-quality ab-initio approaches incorporating both relativistic andcorrelation effects to high-orders are discussed. The most reliable treatment of relativitystarts from the first-principles four-component no-pair Dirac-Coulomb-Breit (DCB)Hamiltonian. Multireference correlation schemes presented include the Fock-spacecoupled-cluster (CC) method, equation-of-motion (EOM-CCSD) and many-bodyperturbation theory.

Calculations of energies (e.g. excitation and dissociation energies) and otherproperties (e.g. nuclear quadruple moments) of some heavy atomic and molecular systemsare presented. A detailed study of the influence of nonadditive effects of relativity andelectron correlation on atomic and molecular properties is provided.

60

P14

The Generalized Active Space (GAS) configuration interaction conceptin two-component relativistic theory

Timo Fleig, Theoretical Chemistry, University of Bonn, GermanyJeppe Olsen, University of Aarhus, Denmark

Christel M. Marian, GMD-SCAI, St. Augustin, Germany

Features of the development and first applications of a two-component double group CIprogram are presented [1]. The code includes the determination of natural spinors bydiagonalising the spin-dependent one-particle density matrix and re-running the CI withintegrals transformed into the basis of these natural spinors. By several of these iterations,a significant part of the spin-dependent relaxation in the space of the one-particlefunctions can be made accessible in addition to the spin-dependent optimisation of thewave function in configuration space. The program is based on determinants constructedfrom molecular or atomic two-spinors. The spinor space may be subdivided into anarbitrary number of active spaces (GAS method) with desired occupation constraints, thusmaking a flexible treatment of compounds with different chemical properties feasible.The use of time-reversal and double group symmetries throughout the whole formalismallow for computational savings and are necessary for a theoretically consistentrepresentation [2].Spin-orbit integrals for the computations are provided through an approximativetreatment of the two-electron contributions employing a mean-field approach [3,4,5]. Theapproach has proven to be extremely reliable and furthermore allows for the use of theplain operator of the Coulomb repulsion in the two-electron parts of the CI code, againleading to considerable savings and also to a simplification of the formalism.

References:

[1] T Fleig, J Olsen, and C M Marian. The Generalized Active Space (GAS)configuration interaction concept in two-component relativistic theory: Developmentand first applications. in preparation, 1999.

[2] T Fleig, C M Marian, and J Olsen. Spinor optimization for a relativistic spin-dependent CASSCF program. Theoret. Chem. Acc., 97,1-4:125, 1997.

[3] AMFI, an atomic mean-field spin-orbit integral program, University of Stockholm,1996. Bernd Schimmelpfennig.

[4] B A Heß, C M Marian, U Wahlgren, and O Gropen. A mean-field spin-orbit methodapplicable to correlated wavefunctions. Chem. Phys. Lett., 251:365, 1996.

[5] Christel M Marian. program GENMFINT, Bonn, 1997.

Furthermore:

T Fleig and C M Marian, Relativistic ab-initio calculations on PdH and PdD: Therovibronic spectra and rotational splittings, J. Chem. Phys., 108:3517, 1998

61

P16

Relativistic Density Functional Calculations on Large MoleculesContaining Actinides

Laura Gagliardi

Dipartimento di Chimica Fisica ed Inorganica, Viale Risorgimento 4, 40136 Bologna,Italy

Nicholas C. Handy, Andrew G. Ioannou, Chris-Kriton Skylaris, Steven Spencer,Andrew Willetts

Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK

Adrian M. Simper

BNFL, Springfield, Preston, PR4 OXJ, UK

We present some relativistic density functional calculations on some uranium andplutonium complexes, which can be used in the solvent extraction process. The newquantum chemistry code MAGIC has been used to determine energetics and geometriesof Pu-thenoyltrifluoro-acetone, Pu-ethylenediamine-tetraacetate, Pu-diethylenetramine-pentaacetic-acid, and the analogous U-compounds. MAGIC is briefly described and theresults on these complexes in the gas phase and in a liquid environment are presented.Some general principles concerning how to find the most suitable extractant for thevarious actinides in different oxidation states are discussed.

62

P17

MCDF calculations of transition rates of astrophysical interest inneutral Technetium.

M.R. Godefroid1 and Charlotte Froese Fischer2

1 Laboratoire de Chimie Physique Moléculaire, CP160/09Université Libre de Bruxelles, 50 av. F. Roosevelt, B-1050 Bruxelles, Belgium

2 Department of Computer Science, Vanderbilt UniversityBox 1679 B, Nashville, TN 37235, U.S.A.

Technetium lines and oscillator strengths have a high astrophysical interest in the study ofS-type stars [1]. Semi-empirical calculations of transition rates for selected lines in Tc Ihave been performed by Garstang [2] using the parametric study of energy levels forgetting the wave function compositions. We will assess their reliability by performing abinitio calculations in the relativistic multiconfiguration Dirac-Fock (MCDF) scheme,using the GRASP94 code [3].

[1] Jorissen A., private communication (1998)[2] Garstang R.H., Publ. Astron. Soc. Pacific. 93 641 (1981)[3] Parpia F., Froese Fischer C. and Grant I.P., Comput. Phys. Commun. 94 249 (1996)

63

P18

Computational methods for four-component molecular calculations

Harry Quiney(1) and Ian Grant(2)

(1) School of Chemistry, University of Melbourne, Parkville, Victoria, 3052, Australia(2) Mathematical Institute, University of Oxford, 24/29 St. Giles', Oxford OX1 3LB, UK

We describe computational methods used in BERTHA, our relativistic molecularelectronic structure program. Algorithms have been developed which allow us to workdirectly with a basis of spherical Gaussian spinor functions (G-spinors), building on ourextensive experience in atomic structure theory, in particular the exploitation oftechniques of Racah algebra in evaluating one-centre integrals.

We discuss strategies for efficient construction of the Fock matrix in four-componentself-consistent field calculations, including the exploitation of the kinetic balanceprescription in the construction of the J-matrix. The contribution made by relativistic one-centre integrals and ways of reducing the computational effort, with integral screeningalgorithms and by the use of approximate molecular potentials in intermediate iterations,are all discussed. We indicate how properties which depend on the current density,including magnetic effects and the Breit interaction, have been incorporated in ourformulation.

Our relativistic many-body procedure, based on a direct implementation of many-bodyperturbation theory, is then described, and we present our preliminary implementation offour-component relativistic density functional theory.

The computational scheme is illustrated by calculations drawn mainly from problems inmolecular physics, including parity and time reversal symmetry in diatomic molecules,parity-violating interaction energies in chiral molecules, shielding tensors in nuclearmagnetic resonance, x-ray transition energies in open-shell systems, and studies of therelativistic modification of the molecular momentum density, which has a significanteffect in the (e,2e) spectroscopy of systems containing heavy elements.

64

P20

Theoretical study of some lanthanide (III)-polyazamacrocyclic chelatesfor magnetic resonance imaging.

Elsa S. Henriques, Margarida Bastos, Carlos F. G. C. Geraldes and M. Joao Ramos

Departamento de Quimica, Faculdade de Ciencias, Universidade do Porto, Rua doCampo Alegre, 687, 4169-007 PORTO, Portugal

A set of parameters consistent with the CHARMM force field has been determined formolecular dynamics simulations of several DOTA- and DOTP- Ln (III) chelates.Bonding and van der Waals parameters were derived from the available experimentaldata and analogy to similar ones in the existing force field. Net atomic charges werederived from ab initio calculations to reproduce molecular electrostatic potentials (ESPs),with an effective core potential (ECP) basis set for the metal ion and the 6-31G* basis setfor the ligand atoms. The charges are consistent with the TIP3P water model.Preliminary molecular dynamics simulations of the lanthanide chelates in aqueoussolution were performed using the Nose-Hoover thermostat at 300K. The new parameterscorrectly predicted the molecular structures and stability of the chelates major and minorisomers.

65

P21

Multiconfiguration Dirac-Fock calculation of 1s2p 1P1 and 1s2p 3P1levels in the high Z helium-like ions.

L. de Billy , S. Boucard and P. Indelicato

Laboratoire Kastler-Brossel, Case 74, Universiti P & M Curie, 4 place Jussieu, F-75252Paris CEDEX 05 France

The helium-like heavy ions are important test systems for the relativistic many-bodycalculation. Some difficulties on the calculation of the 1s2 and 1s2s 3S1 levels associatedto the relativistic structure of the multiconfiguration dirac-fock (MCDF) method wereresolved [1,2]. Following these works, we study the convergence problem in thecalculation of the 1s2p 1P1 and 1s2p 3P1 levels for Z=80. It appears that a perturbativetreatment of the retardation term in the electron-electron correlation is not possible at highZ. It is necessary to include this term in the wave function and potential calculations (i.e.in the self-consistent process of the MCDF calculation).

[1] P. Indelicato, Physical Review A 51 [2]: 1132-1145 (1995)[2] P. Indelicato, Physical Review Letters 77 [16]: 3323-3326 (1996)

66

P22

Quadratic Dirac-Hartree-Fock response.

P. Norman and H. J. Aa. Jensen

Department of ChemistryUniversity of Southern Denmark (Main campus: Odense University)

Campusvej 55, DK-5260 Odense M, Denmark

We have derived and implemented expressions for the frequency dependent quadraticresponse function for the 4-component all-electron Dirac-Hartree-Fock model in theDirac program package [http:/dirac.chem.ou.dk/dirac]. With this model one can forinstance calculate second harmonic generation (SHG) hyperpolarizabilites. A bigadvantage of this formulation compared to a non-relativistic formulation with relativisticcorrections is that the pole structure will correspond to Dirac-Hartree-Fock RPA and notto non-relativistic RPA. Theory and sample calculations will be presented.

67

P24

Ab initio calculation of the molecular field and spin orbit splitcomponents of L2,3VV Auger spectra

Mika Kivilompolo, Reinhold F. Fink*, Helena Aksela and Seppo Aksela

Department of Physical Sciences, University of Oulu, FIN-90570 Oulu, Finland* Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Ab initio calculations based on quantum chemical methods and the one-centreapproximation have been carried out for the L2,3VV normal Auger spectrum of HCl. Spinorbit and molecular field effects [1-4] were explicitly included in the description of theintermediate 2p-1 core hole state. The results were compared with the experimentalspectrum obtained with synchrotron radiation. L2,3VV transitions were also studied in theisoelectronic argon atom. The calculated Auger spectra are in good agreement to theexperimental and to prior theoretical results [5-6].

For HCl the calculations predict substantially different total Auger transition probabilitiesfor the three non-degenerate spin-orbit and molecular field split 2p-1 states. Total decayrates of 126, 99 and 113 meV were obtained for the 2p3/2

-1 (2Π3/2), 2p3/2-1 (2Σ1/2), and 2p1/2

-1

(2Π1/2) core hole components. Furthermore, each of these core hole states gives rise toremarkably different intensity distributions.

These effects are explained by (i) the partial orientation of the chlorine 2p-1 core holestates by the molecular field, (ii) a decrease of the net population of the chlorine 3porbital in the bond direction due to the chemical bond, and (iii) the clear 97% preferenceof the Auger decay of an oriented 2p core orbital to produce final states with at least onehole in the 3p orbital with the same spatial orientation.

References

[1] S. Svensson, A. Ausmees, S. J. Osbourne, G. Bray, F. Gel'mukhanov, H. Ågren, A.Naves de Brito, O.-P. Sairanen, A. Kivimäki, E. Nõmmiste, H. Aksela, and S. Aksela,Phys. Rev. Lett. 72 (1994) 3021.

[2] F. Gel'mukhanov, H. Ågren, S. Svensson, H. Aksela, and S. Aksela, Phys. Rev. A 53(1996) 1379.

[3] H. Aksela, E. Kukk, S. Aksela, O.-P. Sairanen, A. Kivimäki, E. Nõmmiste, A.Ausmees, S. J. Osborne, and S. Svensson, J. Phys. B 28 (1995) 4259.

[4] M. Siggel, C. Field, L. Sæthre, K. Børve, and T. D. Thomas, J. Chem. Phys. 105(1996) 9035; K. Børve, Chem. Phys. Lett. 262 (1996) 801.

[5] O. M. Kvalheim, Chem. Phys. Lett. 98 (1983) 457.[6] E. Z. Chelkowska and F. P. Larkins, At. Data Nucl. Data Tables 49 (1991) 121.[7] R. F. Fink, M. Kivilompolo, H. Aksela, and S. Aksela, Phys. Rev. A 58 (1998) 1988.

68

P28

Calculation of Spin-orbit coupling constants using the SymmetricGroup Approach of Configuration Interaction.

Thomas la Cour Jansen, S.Rettrup, J.G.Snijders, P.Palmieri, C.R.Sarma

Laboratory of Chemical Physics and Materials Science Centre, University of Groningen,The Netherlands

A method for evaluating spin-dependent one-electron properties using the symmetricgroup approach for configuration interaction will be presented briefly. A mean-field one-electron operator and spin-orbit coupling constants using this operator as a perturbation ofthe CI-wavefunctions will be presented for various species.

69

P29

Hermitian Coupled-Cluster Approach

Arik Landau


The Hermitian coupled-cluster approach (CCA) based on the Jørgensen condition leadsto a formalism where the exact as well as the model space determinants are orthonormal,with a Hermitian effective Hamiltonian. This is not the case in the traditional intermediatenormalization (IN) approach. In the IN non-hermiticity may also be caused by truncation,leading to non-hermiticity of the wave operator, so the approximate wave functions arenot orthogonal. It is possible to present a CCA which is Hermitian at all truncations. Thishas the consequence that additional terms, not present in the conventional treatment,appear at each truncation, making these truncations generate more 'physical', moresymmetric and more complete expansions. The additional terms include intermediatestates that reach beyond the approximation employed. In our calculations, using the pairapproximation through third order, additional terms include some three-body excitationsin the intermediate states; in the traditional approach the triples approximation is neededto take these terms into account. The resulting wave functions in this method (theeigenstates of the Hermitian coupled-cluster Hamiltonian) are orthonormal in anytruncation.

70

P30

Two-Component Spin-Orbit Calculations for the Molecules ContainingHeavy or Superheavy Atoms

Yoon Sup Lee

Department of Chemistry and Center for Molecular ScienceKAIST, Taejon, 305-701 Korea

Relativistic effects become important for the correct description of electronic structures ofmolecules containing heavy atoms. Spin-orbit effects may be regarded as part ofrelativistic effects, and also become increasingly important for heavy atoms and systemscontaining heavy atoms. We have been working on ab initio molecular orbital(MO)methods which take spin-orbit and other relativistic effects into account without too muchcomputational effort by using relativistic effective core potentials(REPs). In addition toour own REP packages[J. Comp. Chem. 13, 595(1992); Chem. Phys. Lett., 253,216(1996); J. Comp. Chem., 19, 1526(1998)], we recently modified the MOLFDIRpackage by L. Visscher et al. to use one-electron integrals of relativistic effective corepotentials with(REP method) and without(AREP method) spin-orbit operators[Chem.Phys. Lett., 293, 97(1998); J. Chem. Phys. 109, 9384(1998)]. In both packages, integralsover REPs are computed by the ARGOS program. The modified MOLFDIR packageperforms two-component REP calculations instead of two-component non-relativisticcalculations intended in the original package. These two-component methods are referredto as REP and/or Kramers’ restricted(KR-) methods to be consistent with our previouswork and include spin-orbit interactions from the HF level of theory. Therefore, REPcalculations are directly comparable to all-electron relativistic calculations employing theDirac operator. In addition, comparison of AREP and REP results from the presentmethods allows a consistent and well-defined estimate of spin-orbit effects at variouslevels of theory. REP and AREP calculations of selected diatomic and small polyatomicmolecules of sixth-row and superheavy elements will be discussed with the primaryemphasis on spin-orbit effects on the ground state properties.

71

P31

Relativistic MCSCF by means of direct perturbation theory : theoryand implementation

Wenjian Liu and Werner Kutzelnigg

Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum,Germany

E-mail: [email protected]

The treatment of relativistic effects for heavy atom containing systems has beendominated by nonperturbative approaches. However, relativistic perturbation theory(RPT) is still appealing since for most of the chemically interesting systems relativisticeffects are just a perturbation. The usefulness of RPT is on the other hand to providedetailed information for the understanding of the electronic structure. The reason whyRPT had not become popular before nonperturbative approaches were picked up was dueto the problems within the Foldy-Wouthuysen (FW) transformation, which in principlecan only be applied to the first order. RPT has become renaissant due to the elaboration ofthe so-called 'direct perturbation theory' (DPT). Here, the inverse of the speed of light (c-

1) directly serves as the perturbation parameter. The spurious singularites of the FWtransformation are avoided to all orders of the perturbation series. Although to the firstorder (O(c-2)) the FW approach is equaivalent to DPT in a complete basis set, DPTconverges much faster to the exact value and is thus more accurate when finite bases areused.So far the ab initio (wavefunction based) DPT has been applied only to closed-shellstates. The scalar first order DPT terms in a restricted active space (RAS) scheme wererecently implemented into an numerical atomic program by Sundholm and Ottschofski,where the 2-electron Darwin term was explicitly calculated and thus is not a pure DPT.Previously DPT was derived only for (nondegenerate) closed-shell states. We haveextended DPT to open-shell states in terms of effective Hamiltonians, which is aconvenient choice for (quasi-)degenerate states. In this contribution the first order DPT atthe CASSCF level is implemented on the fly of the MOLPRO package so that ab initioDPT can be applied to open-shell states for the first time. Results for the spectroscopicconstants are reported for the molecules of X2 (X = F, Cl, Br, At) and TlX (X = F, Cl, Br,I) to compare to other relativistic calculations.

72

P32

Electron structure of complexes containing f elements : a DFT studyincluding scalar relativistic effects.

Carlo Adamo and Pascale Maldivi

Laboratoire de Reconnaissance IoniqueService de Chimie Inorganique et Biologique

Département de Recherche Fondamentale sur la Matière CondenséeCEA-Grenoble, 17 Rue des Martyrs 38054 Grenoble Cedex 9 France

The description of the interactions between a trivalent lanthanide ion (Ln3+) oractinide ion (An3+) and its chemical environment is a key-point in the area of nuclear fuelwaste disposal, especially for the design of actinide selective extractants. Indeed, Ln3+

ions give mainly ionic interactions, whereas An3+ ions may bring some covalent characterwhen it is bonded to a polarisable ligand.

Our aim is therefore to describe by quantum chemistry the metal-ligand bondingfor both series of f elements, by studying the influence of the ion and of the ligand. Weuse the Kohn-Sham formalism to take into account some dynamic correlation, withgradient corrected exchange and correlation potentials (Generalized gradientapproximation). Some exact exchange was also included with hybrid functionals such asB3LYP. Relativistic effects are taken into account either through an effective corepotential, or by a pertubational treatment of valence electrons using the quasi-relativistichamiltonian including mass-velocity and Darwin terms (Amsterdam Density Functional2.3.01).

The M-L bonding has been studied with Mulliken atomic charges and by a NPA(Natural Population Analysis), but also by an estimation of the electrostatic and orbitalinteractions (Ziegler et al.2 method in ADF).

Results of various computations on LnX3 (Ln = La, Gd, Lu, X : F à I) systems willbe described3 : they show a very good agreement with experimental values. The analysisof the electron structure shows a strongly ionic interaction, even if some weak covalentcharacter appears with a polarisable ligand such as Br- ou I- . This study also shows theneed for a combined approach, by evaluating both electron transfer as well as the relativeamount of electrostatic and orbital interaction energies.

Within the same framework, the electron structure of complexes with N-heterocyclic ligands will be described.

1. ADF 2.3.0. Theoretical Chemistry, Vrije Universiteit, Amsterdam; Baerends, E. J. etal. Chem. Phys. 1973, 2, 41.

2. Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1.3. Adamo, C ; Maldivi, P. J. Phys. Chem. 1998, 102, 6812.

73

P33

Relativistic Fock Space Coupled-Cluster Calculations for Moleculeswith Heavy Elements: ThF4 and AuH .

G. Mallia, J. Styszynskia, E. Eliavb, U. Kaldorb and L. Visscherc

a Department of Chemistry, Simon Fraser University, Burnaby, V5A1S6, BC, Canadab School of Chemistry, Tel Aviv University, 69978, Tel Aviv, Israel

c Department of Chemistry, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, TheNetherlands

The four-component relativistic coupled cluster method is based on the Dirac-Coulom-Breit Hamiltonian and includes correlation by Fock-Space coupled-cluster with singleand double excitations (FS-CCSD). The method has been applied to the AuH, ThF4 and

their ions. The Dirac-Fock wavefunctions for an appropriate reference closed shell statewere obtained by the MOLFDIR package [1] in the universal Gaussian basis [2].Correlation energies for states of interest were calculated by applying the molecularrelativistic FS-CCSD program [3] according to the following schemes:

AuH++(0,0) _ AuH+(0,1) _ AuH(0,2)

AuH++(2,0) _ AuH+(1,0) _ AuH(0,0) _ AuH-(0,1)

ThF4+(1,0) _ ThF4(0,0) _ ThF4-(0,1)

Equilibrium bond distances, adiabatic ionization potentials, electron affinities,frequencies and bond energies were calculated. Good agreement with experiment wasobtained.

References:

[1] L. Visscher, O.Visser, P.J.C. Aerts, H. Merenga, and W.C. Nieuwpoort, Comp. Phys.Commun. 81, 120 (1994)

[2] G.L.Malli, A.B.F.Da Silva and Y.Ishikawa, Phys. Rev. A 47, 143(1993)[3] E. Eliav, U. Kaldor, Chem. Phys. Lett. 248, 405 (1996)

74

P34

The thermodynamics of actinide oxides

Valérie Vallet, Laurent Maron, Thierry Leininger, Christian Teichteil

Laboratoire de Physique Quantique, IRSAMC,UMR 5626, Université Paul Sabatier,

118, route de NarbonneF-31062 Toulouse cedex, France

Bernd Schimmelpfennig, Ulf Wahlgren,

Institute of Physics, Stockholm University,P.O. Box 6730

S-11385 Stockholm, Sweden

The investigation of complexes involving actinide atoms is a new challenge fortheoretical chemistry. Due to the large number of electrons to correlate and thecomplexity of the electronic structure (open f-shell), one has to check the performances ofthe standard quantum chemistry methods. Nevertheless, the main problem is the poor setof experimental data available on the gas phase because of the high difficultiesencountered to carry out experiments on actinide compounds.

In this poster, we present a systematic study of the gas phase thermodynamicproperties of early actinide oxides and we compare the results with the rare data available.We also got information on ionisation potentials of the actinide atoms as well as themonoxides and dioxides. Our results obtained at the RECP-AQCC level are in perfectagreement with experimental values. A general trend along the series is observed anddiscussed.

75

P35

High precision test of parity violation in the spectrum of the chiralmolecule CHFClBr

T. Marrel, Ch.Daussy, M. Ziskind, Ch.J. Bordé and Ch. Chardonnet

Laboratoire de Physique des LasersUniversité Paris-Nord, avenue J.-B.Clément

93430 Villetaneuse, France

A laser nonlinear spectroscopy experiment has been designed and implemented to test theconjecture that enantiomers of chiral molecules may have different spectra because of theparity violation associated with neutral currents in the weak interaction between electronsand nuclei. We have conducted preliminary experimental tests on hyperfine componentsof vibration-rotation transitions of CHFClBr in the 9.3 µm spectral range. Thefrequencies of saturation resonances of separated enantiomers have been compared andfound identical within 13 Hz (∆ν/ν<4.10-13). Though the theoretical background of thedegeneracy lifting induced by the weak interaction in molecules is well established, thequantitative evaluation of the expected effect on rovibrational transition frequenciesremains a challenge today. We therefore undertake an extension of the current models,adapted only to calculate the induced shift of the electronic ground states of eachenantiomer of a chiral molecule, in order to estimate how rotational and vibrational levelsare affected in molecules, which is of greater interest in an experimental concern.

76

P37

Ab initio calculations of the NpO22+ and NpO2

+ ions.

Spiridoula Matsika and Russell M. Pitzer

We are studying the relativistic effects on molecular systems through ab initio spin-orbitconfiguration interaction calculations based on relativistic effective core potentials.The electronic spectra of the linear NpO2

2+ and NpO2+ ions are being calculated. The

ground state of NpO22+ is 5/2u (2∆u + 2Φu). Equilibrium distances and symmetric-stretch

vibrational frequencies have been obtained and compared with experiment. In the lowerenergy part of the spectrum lie the ƒ → ƒ transitions while the first charge-transfer state isat 18,000 cm-1. NpO2

+ has one more electron which alters both the ground state and thespectrum significantly. The ground state is 4g (3H4g, δuφu) with equilibrium distanceslarger than the NpO2

2+ ion and symmetric-stretch vibrational frequencies smaller.Preliminary results indicate that there are many ƒ → ƒ states and the first charge-transferstate is above 20,000 cm-1.NpO2

2+ has been experimentally studied in the Cs2U(Np)O2Cl4 crystal. We are modelingthis crystal and repeating the calculations; this will incorporate the effects of the differentions surrounding NpO2

2+.

77

P38

A Self-Consistent Two-Component Density Functional Implementationof Spin-Orbit Coupling within the Douglas-Kroll-Hess Scheme.

Application to Diatomic Molecules

Markus Mayer, Notker Rösch

Lehrstuhl für Theoretische Chemie, Technische Universität München, D-85747Garching, Germany

An extension of the two-component Douglas-Kroll-Hess approach to densityfunctional theory [1] is presented which takes spin-orbit interaction into account in a self-consistent and variational fashion. The scheme was incorporated into our programParaGauss for parallel computers [2]. In this implementation relativistic corrections to theelectron-electron interaction are neglected. It is demonstrated that this approachreproduces spin-orbit splittings of p- and d-shells of heavy elements very well, whileproblems arise for f-shells.

Open-shell systems are treated self-consistently by defining density functionalswith respect to the 2x2 spin-density matrix [3] rather than only with respect to itsdiagonal elements, the spin-up and spin-down densities [4]. The resulting exchange-correlation potentials have contributions off-diagonal in the spin components.

The new method has been applied to diatomic molecules containing heavyelements of the rows V and VI. For the molecules Au2, Bi2, Pd2, PbO, HgO, PtH, and TlHbond lengths, harmonic frequencies, and binding energies have been determined. Theobtained spin-orbit effects are very close to those of the two-component ZORA scheme[5]. Spin-orbit effects on bond lengths and harmonic frequencies are rather small and thusnot significant, On the other hand, binding energies, especially for Bi2, PbO, and TlH, aredrastically improved when spin-orbit interaction is taken into account. This is mainly dueto the open-shell atomic reference systems and corroborates their correct treatment by ourapproach.

The scheme was also applied to the low lying exited states of PtH. For excitationenergies excellent agreement is achieved with results of correlated Dirac-Hartree-Fockand Douglas-Kroll-CI calculations.

Finally the density of states of highly symmetric gold clusters was investigated.The spin-orbit splitting of the valence d-band shows satisfactory agreement withphotoelectron spectra of related systems.

[1] N. Rösch, S. Krüger, M. Mayer and V.A. Nasluzov in: Recent Developments andApplications of Modern Density Functional Theory, J.M. Seminario (editor), Elsevier(1996).

[2] Th. Belling, Th. Grauschopf, S. Krüger, M. Mayer, F. Nörtemann, M. Staufer, C.Zenger, N. Rösch, in: High Performance Scientific and Engineering Computing; H.-J.Bungartz, F. Durst, und Chr. Zenger (eds.), Lecture Notes in Computational Scienceand Engineering, Springer Verlag, Heidelberg, 1999.

[3] A. Görling, Phys. Rev. A. 47, 2783 (1993).[4] M. Mayer, A. Görling, and N. Rösch, to be published.[5] E. van Lenthe, J.G. Snijders and E.J. Baerends, J. Chem. Phys. 105, 6505 (1996).

78

P39

Relativistic Gaussian basis sets and molecular relativistic calculations

Jan Micanko and Stanislav Biskupic

Department of Physical Chemistry, Slovak Technical University812 37 Bratislava, Slovak Republic

e-mail: [email protected]

A method for the Gaussian basis sets generation for molecular relativistic Dirac-Fockcalculations is proposed. The basis set exponents are obtained in process of a stochasticoptimization (a hybrid of simplex and simulated annealing optimization technique hasbeen employed) of a functional defined as the sum of squares of differences between thenumerical relativistic atomic wave functions and the wave functions obtained by ordinarygradient energy-functional based procedure. The present method seems to be veryeffective and robust. As an example the optimized basis sets of atoms from H to Ar andCu, Ag, Au are presented. Moreover, the bond lengths, dissociation energies andharmonic vibrational frequencies of the electronic ground state of hybrides CuH, AgH,AuH, have been evaluated with a variety of ab initio methods.

79

P42

Numerically exact Dirac-Coulomb ground state energies of helium-likeions.

Grzegorz Pestka

Instytut Fizyki, Uniwersytet Mikoaja Kopernika,Grudzidzka 5, PL 87-100 Torun, Poland

Ground-state energies of helium-like atoms are derived from the Dirac-Coulomb equationusing a mini-max-type variational principle. The approach may be considered as arelativistic generalization of the Hylleraas-CI method. The trial wave-functions areconstructed as kinetically balanced combinations of explicitly correlated 16-componentspinors fulfilling correct boundary conditions at r ô 0, r ô • and r12 ô 0. The energiesobtained are equal to the eigenvalues of the Dirac-Coulomb Hamiltonian with theaccuracy of 8 significant figures.

80

P43

A quantum chemical approach to QED

Ian Grant (1) and Harry Quiney (2)

(1) Mathematical Institute, University of Oxford, 24/29 St. Giles', Oxford OX1 3LB, UK(2) School of Chemistry, University of Melbourne, Parkville, Victoria, 3052, Australia

The BERTHA code[1] depends for its efficiency on exploitation of the rich internalstructure and group-theoretical properties of Dirac central-field spinors which make thefour-component analogues of Gaussian basis functions (G-spinors) so powerful in atomicand molecular structure. This code is being applied to a rapidly increasing range of smallmolecules, and to the evaluation of several molecular properties including g-factors,nuclear magnetic resonance shielding tensors[1], hyperfine coupling constants and parityviolating effects[2,3].We shall present applications of BERTHA to molecules containing heavy elements, andatomic results obtained by exploiting large basis sets of L-spinors [4]. Despite recentclaims to the contrary, L-spinor functions are valid two-component spinor sets derivedfrom four-component solutions of the Dirac-Coulomb Sturm-Liouville equation. High-precision bound-state solutions obtained using these finite basis set techniques form animportant part of our approach to the calculation of the Lamb shift, which uses our partialwave renormalization procedure[5].Sample calculations will include

• Atomic x-ray form factors and dipole polarizabilities• Pseudo-spectral photoionization profiles• (e,2e) momentum profiles for molecules• NMR shielding tensors in heavy element molecules• Atomic Lamb shift

References:

[1] H M Quiney, H Skaane & I P Grant, Adv. Quant. Chem. 32, 1-49 (1998); J. Phys. B30, L829-834 (1997).

[2] H M Quiney, H Skaane & I P Grant, J. Phys. B 31, L85-95 (1998).[3] H M Quiney, H Skaane & I P Grant, Chem. Phys. Letts. 290 473-480 (1998).[4] I P Grant in Relativistic, QED and Weak Interaction Effects in Atoms p. 240, (ed. W R

Johnson et al. ), Conference Proceedings No. 189 (New York, American Institute ofPhysics, 1989); in X-ray and Inner-shell Processes , pp.46-71 (ed. T Carlson et al. ),Conference Proceedings No. 215, (New York, American Institute of Physics, 1990);in Effects of Relativity in Atoms, Molecules & the Solid State pp. 17-43, (ed. S Wilsonet al. ), (New York, Plenum 1991).

[5] I P Grant and H M Quiney, Phys. Scripta T 46, 132-138 (1993); H M Quiney and I PGrant, J. Phys. B 27, L299-L304 (1994); I P Grant and H M Quiney, J. Phys. A 26,7547-7562 (1993).

81

P44

Ab-Initio Calculations With Effective Core Potentials On Terpyridine-Ln(III) Complexes.

C. Rabbe, J.P. Dognon

Commissariat à l'Energie Atomique, Valrhô - Marcoule, DCC/DRRV/SEMP/LCTS, F-30207 Bagnols/Cèze, France.

There is much current interest in the separation of actinide (III) and lanthanide(III) by solvent extraction in the field of nuclear fuel reprocessing. The understandings ofmetal - ligand interaction is, though, of great importance in the design of new ligands.

Ab initio calculations with effective core potentials (ECP) have been carried outon 1:1 complexes of terpyridine (tpy) with lanthanide (III). First of all, fourpseudopotentials [1-4] with 4f orbitals included in the core have been compared for thecalculation of La(tpy)3+ complexes. The comparison of relativistic and non relativisticECPs has also been performed.

With the Dolg's quasirelativistic pseudopotential [2], the variation of severalproperties of Ln(tpy)3+ complexes has been studied for the whole lanthanide series. It hasbeen shown a linear variation for all properties (geometrical and energetical) except forMulliken charges on the metal atom.

Calculations have also been performed on three complexes of known X-Raycristallographic structure. The experimental and calculated geometries have beencompared. For all structures, the calculated metal -ligand bond distances are within 0.2 Åcompared to experimental one. In any cases, the relative order from one complex toanother is conserved.

Finally, some calculations with small core effective potentials (i.e. with 4f orbitalsin the valence) have been started. The results will be compared with the former ones.

[1] P.J. Hay, W.R. Wadt, J. Chem. Phys., 82(1), 299 (1985).[2] M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys., 90(3), 1730 (1989).[3] R.B. Ross, J.M. Powers, T. Atashroo, W.C. Ermler, L.A. LaJohn, P.A. Christiansen, J.

Chem. Phys., 93(9), 6654 (1990).[4] T.R. Cundari, W.J. Stevens, J. Chem. Phys., 98(7), 5555 (1993).

82

P45

The charge transfer in small ion-molecule systems : calculation andmodeling

Sophie Hoyau(1,2), Valérie Brenner(1), Jean-Pierre Dognon(2), Philippe Millié(1)

(presented by C. Rabbe)

(1) Laboratoire de Chimie Théorique, DSM/DRECAM/SPAM, CE Saclay, 91191 Gif-sur-Yvette Cedex

(2) Laboratoire de Chimie Théorique et Structurale, DCC/DRRV/SEMP, CE Valrho, BP171, 30207 Bagnols-sur-Cèze Cedex

Finding new extracting molecules which allow to separate lanthanide (Ln) from actinide(An) trivalent cations is a matter a high interest for the nuclear fuel reprocessing. Indeedthose cations show same charges, similar ionic radii, and small polarizabilities. The largercovalent character of the bond between actinide cations and organic ligands seems to be aclue to separate these two series: the larger the covalence, the larger the charge transfer tothe ligand. In order to perform molecular dynamic calculations on Ln and An trications-containing systems, it is consequently essential to include the charge transfer (CT) nevertaken into account in the usual model potentials. So we aimed at evidencing, quantifyingand modeling the CT contribution to the interaction energy. The H2O-M2+ (M = Ca, Zn,Cd, Hg) systems have first been studied as simple model systems. Relativistic EffectiveCore Potentials have been used to describe the cations. A decomposition of theinteraction energy into electrostatic, polarization, repulsion and CT contributions hasbeen undertaken at the Hartree-Fock level for various ion-molecule types of approach. Atthe equilibrium geometry, the CT determined is important for all of the cations exceptCa2+. The Molecular Orbitals (MO) involved in the CT have been evidenced thanks toNBO population analyses. Finally, a simple relationship has been determined betweentheir overlap integrals and the CT. The same approach is now applied to lanthanidetrications containing systems, beginning with H2O-M3+ (M = La, Eu, Lu) systems. TheCT determined is non negligible even for lanthanide cations. The electron transfer occursfrom the oxygen lone pairs to the (n-1)d orbitals of the cation (instead of the ns orbital forthe dications previously studied). A relationship between the CT and the overlap integralsof the fragments MOs involved is then more complicated to evidence.

83

P46

The frequency-independent Breit interaction in relativistic atomicstructure calculations

Markus Reiher, Juergen Hinze, and Dirk Andrae

Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld,Postfach 10 01 31, D-33501 Bielefeld, Germanyf

We present a reformulation of the frequency-independent Breit interaction operator inspherical coordinates and the corresponding matrix element over spinors used in atomicstructure calculations. With this formulation it becomes possible to compute the matrixelements of the Breit interaction efficiently and analogous to those of the Coulombinteraction, i.e. by determining the corresponding interaction potential functions using thePoisson equation and a modified analogue of it. An effective algorithm for suchcalculations using numerical shell functions for the radial parts of the spinors ispresented.The derived formulae are simplified compared to previous formulations [1]. Our resultscan be extended readily to electronic structure calculations for molecules. They willsimplify equally computations using either basis-sets or a numerical representation of theorbitals such that the Breit interaction can be included effectively in numerical CI andSCF calculations for atoms.

f E-mail: [email protected], [email protected] [email protected]

[1] I. P. Grant, Adv. Phys. 19 (1970) 747-811; I. P. Grant, N. C. Pyper, J. Phys. B 9(1976) 761-774

84

P47

Total binding energies of Cs ions. A comparison betweenMulticonfiguration Dirac-Fock and Relativistic Many Body

Perturbation Theory correlation energies.

G. Rodrigues, P. Indelicato, E. Lindroth

Laboratoire Kastler-Brossel, Case 74, Université P&M Curie, 4 place Jussieu, F-75252Paris CEDEX 05 France.

Atomic Physics, Stockholm University, Frescativ gen 24, S-104 05 Stockholm

With the use of penning traps, combined with heavy ions sources, it has become possibleto measure total masses of atomic ions with accuracy of the order of 1ppb or better. Atthat level of accuracy total atomic binding energies of ions must be calculated accuratelyto enable to compare the masses of different ions or to deduce the atomic mass. Accuratemass measurement of Cs are needed for the measure of h/m (h Plank constant, m electronmass) from the study of the recoil of Cs atom absorbing photons. This constant providesan independent method to determine the fine structure constant. In this work we calculatetotal Coulomb and Breit correlation as well as radiative correction contributions to thebinding energy of He-like, Be-like, Ne-like, Ar-like, Kr-like and Xe-like Cs by both theMulticonfiguration Dirac-Fock (MCDF) method and Relativistic Many BodyPerturbation Theory (RMBPT) and compare them. Reasonable agreement is foundbetween both methods for ions up to Ar-like. The MCDF method however has greatdifficulty to compute the inner-shell contribution to correlation for ions with more than 10electrons. From both calculation we provide binding energy accurate to a few eV, whilecurrent experimental precision requires only around 100 eV.

This work is partly funded by the EUROTRAP TMR network.

85

P48

The energy of the relativistic electron-positron field

Norbert Roehrl

Regensburg, Germany

It was shown in [1] that the energy of the relativistic electron-positron field interactingvia a second quantized Coulomb potential in Hartree-Fock approximation is positiveprovided the fine structure constant is not bigger than 4/π. We show that it is instable ifthe fine structure constant is above this critical value. We do this by adapting an idea ofChaix, Iracane and Lions [2]. - This is joint work with Dirk Hundertmark, Princeton, andHeinz Siedentop, Regensburg.

[1] V. Bach, JM. Barbaroux, B. Helffer, H. Siedentop: On the Stability of the RelativisticElectron-Positron Field. mp_arc 98-272, to appear in Communications inMathematical Physics.

[2] P. Chaix, D. Iracane, P.L. Lions: From quantum electrodynamics to mean-fieldtheory: II. Variational stability of the vacuum of quantum electrodynamics in themean-field approximation. J. Phys. B. 22 (1989) 3815-3828.

86

P49

The aurophilic attraction as interpreted by local correlation methods

Nino Runeberg, Martin Schütz and Hans-Joachim Werner

Helsinki, Finland

The nature of the "aurophilic interaction" is studied by applying local second-orderMoeller-Plesset perturbation theory (LMP2) on model dimers of [X-Au-PH3]2 (X=H,Cl)type. The possibility to decompose the correlation contribution of the interaction energyin the dimer (A-B) into different excitation classes reveals that the dispersion contribution(A-A',B-B') is accompanied by an almost equally important ionic component (A-A',B-A'),at shorter distances. Double excitations where at least one electron originates from thegold 5d orbitals, account for almost 90% of the attraction. The relativistic effect amountsto 28 % of the binding energy. The main source for the relativistic stabilization isoriginating from an increase in the attractive contribution involving excitations from theAu 5d shell.

87

P50

On the redox behaviour of actinide compounds in gas phase andsolution

B. Schimmelpfennig(a), L. Maron(b), V. Vallet(b), Th. Leininger(b), O. Gropen(c) andU. Wahlgren(d)

a. Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, D-70569 Stuttgart,Germany

b. Laboratoire de Physique Quantique, I.R.S.A.M.C., Université Paul Sabatier, 118, routede Narbonne, F-31062 Toulouse cedex, France

c. Institute of Mathematical and Physical Science, University of Tromsø, N-9037 Tromsø,Norway

d. Institute of Physics, Stockholm University, P.O. Box 6730, S-11385, Stockholm,Sweden

The preparation and storage of nuclear waste is nowadays a challenge and predictions bytheory might be useful for experimentalists when looking for promising separationschemes or even for handling nuclear fuel at high temperature. We have investigated thereliability of different theoretical approaches to the chemistry of actinide compounds ingas phase and solution for different model and experimentally well-known systems. Thisposter will cover additional material to the talk by Ulf Wahlgren.

88

P51

Wood-Boring ab initio model potential relativistic treatment of Ce andCeO.

Luis Seijo

Dep. de Quimica, C-XIV, Univ. Autonoma de Madrid, 28049 Madrid, Spain

A simple, approximate manner of simultaneously handling the 5s and 6s orbitals in thevalence of the lanthanide elements in Wood-Boring based relativistic ab initio core modelpotential calculations (WB-AIMP), which had been previously formulated with therestriction of having only one valence orbital with a given l, is presented. Its applicabilityis shown in spin-orbit configuration interaction calculations on Ce and spin-freecalculations on CeO. The good quality of the Wood-Boring spin-orbit operators of Ce isshown and a recommended contraction of its valence basis set is established. Theseresults support the production of WB-AIMP data for the lanthanide series. If possible, theWB-AIMP data for the lanthanide and acinide series will be presented.

89

P52

Closed-shell interactions in the systems [MH]2 and [M(C5H5)]2,M=In, Tl

Pekka Pyykkö, Michal Straka

Department of Chemistry, P.O.Box 55 (A.I. Virtasen aukio 1)FIN-00014 Helsinki, Finland

The metallophilic attraction between monovalent Group-13 metal atoms in inorganic ororganometallic systems has received much less theoretical attention than thecorresponding one between coinage metals. We report studies on the title systems usingboth 3-VE and 21-VE pseudopotentials and methods, ranging from MP2 to CCSD(T).Relativistic effects are analyzed using non-relativistic pseudopotentials.Predictions are made for the properties of some hypothetical cyclopentadienyl systems.

90

P55

Multicenter integral calculations for numerically defined orbitals

James D. Talman

Department of Applied Mathematics and Centre for Chemical PhysicsUniversity of Western Ontario, London, Ont. Canada N6A 5B7

In view of the singular behavior at the nuclei of solutions of the Dirac equation forelectrons, methods for the evaluation of multicenter integrals for orbitals that are definedpurely numerically may be of considerable value. In this poster, methods for computingoverlap integrals, nuclear attraction three-center integrals, and electron-electron four-center integrals will be outlined. The methods are based on a numerical prescriptioon forthe expansion of an angular momentum wave function centered at one point in terms ofangular momentum functions centered at another point. This expansion is based on anefficient numerical technique for computing spherical Hankel transforms. Somenumerical results for numerical solutions of the radially symmetric Dirac equation will begiven, and some of the associated mathematical problems will be outlined.

91

P56

Relativistic geometry optimization.

J. Thyssen and H. J. Aa. Jensen

Department of ChemistryUniversity of Southern Denmark (Main campus: Odense University)

Campusvej 55, DK-5260 Odense M, Denmark

We have derived and implemented expressions for the analytic molecular gradient for the4-component all-electron Dirac-Hartree-Fock (DHF) energy in the Dirac programpackage (http://dirac.chem.ou.dk/Dirac). With the gradient it is possible to use quasi-Newton methods for geometry optimization, for example the BFGS method. We haveperformed calculations on a number of mercury compounds. The results are comparedwith both non-relativistic Hartree-Fock (HF) geometries and experimental geometrieswhen available.

92

P57

An effective Spin-orbit –CI treatment

Valérie Vallet, Laurent Maron, Christian Teichteil

Laboratoire de Physique Quantique, IRSAMC,UMR 5626, Université Paul Sabatier,

118, route de NarbonneF-31062 Toulouse cedex, France

& Jean-Pierre Flament

LDMP, UFR de Physique, Bat. P5Université de Lille-1

F-59655 Villeneuve d’Ascq cedex, France

So far, the theoretical spin-orbit interaction treatment can be handled in two ways. In afirst approach, the spin-orbit interaction is considered as a perturbation with respect tocorrelation [1]. A main problem occurs when the radial extension of the spinors is verydifferent like in the thallium atom [2], which obliges to perform a specific correlationtreatment of each spinor. On the other hand, spin-orbit CI method [3], which treatsimultaneously correlation and spin-orbit, can solve this problem but are limited toreasonably small correlation treatment, even if direct algorithms are used.

We suggest an alternative method based on an size-limited effective hamiltonian whichtakes into account correlation effects computed within non relativistic symmetries on alarger space. This hamiltonian is built on the basis of determinants selected by spin-orbitcoupling. We therefore describe the polarisation of the electronic wave function throughspin-orbit interaction. Atomic and molecular tests are presented.

[1] C. Teichteil et al., Chem. Phys. 31, 273 (1983)[2] F. Rakowitz et al., Chem. Phys. Letter 257, 105 (1996)[3] M. Sjøvoll et al., Theor. Chem. Acc. 97, 301 (1997)

93

P58

The quasirelativistic CPD operator in molecular DFT calculations

Christoph van Wüllen

Theoretical Chemistry, Ruhr-Universität, D-44780 Bochum, Germany

The CPD operator [1] is a quasirelativistic two-component Hamiltonian which hasrecently been investigated in some detail by van Lenthe and coworkers [2]. The kineticenergy part of this operator depends on the (effective) potential, and this causes bothformal and practical problems, namely that in the many-electron case the CPD energy isnot stationary with respect to orbital variations and that there is an unphysical response ofthe total energy to small changes of the potential in the cores of heavy atoms. The non-stationarity is not strictly a problem, but leads to additional effort if one wants to calculatefirst-order properties like geometry gradients. The incorrect response to potential changesis a major obstacle, since the energetics of chemical processes like ionization or bond-breaking cannot be calculated directly.These problems can be eliminated using a model potential to construct the kinetic energypart of the CPD operator [3]. For diatomic molecules, it has been shown that this methodreproduces the results of other variants of calculating the CPD binding energy, but thenew method also extends to polyatomic molecules. Geometry gradients have beenimplemented as well [4] such that molecules can now routinely be studied.While this method gives roughly the same results as first-order relativistic calculationseven for 5d elements, it is a substantial improvement if applied to gold and uraniumcompounds, where higher-order relativistic effects are quite important. In a two-component version of the program [5], spin-orbit effects can be treated self-consistently.Comparison with four-component calculations shows that the CPD operator evenperforms well for superheavy elements like eka-gold and its compounds [6].

[1] Akronym built from the names of the authors: Ch. Chang, M. Pélissier, and Ph.Durand, Phys. Scr., 1986, 34, 394

[2] E. van Lenthe, E. J. Baerends, and J. G. Snijders, J. Chem. Phys., 1993, 99, 4597; E.van Lenthe, E. J. Baerends, and J. G. Snijders, J. Chem. Phys., 1994, 101, 9783; R.van Leeuwen, E. van Lenthe, E. J. Baerends, and J. G. Snijders, J. Chem. Phys., 1994,101, 1272; E. van Lenthe, R. van Leeuwen, E. J. Baerends, and J. G. Snijders, Int. J.Quantum Chem., 1996, 57, 281

[3] Ch. van Wüllen, J. Chem. Phys., 1998, 109, 392[4] Ch. van Wüllen, J. Comput. Chem., 1999, 20, 51[5] A. D. Boese and Ch. van Wüllen, unpublished[6] W. Liu and Ch. van Wüllen, J. Chem. Phys., 1999, (in press)

94

P59

The distinction between scalar and spin-orbit relativistic effects

Lucas Visscher and Erik van Lenthe

Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam,De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands

We analyze three different ways of obtaining a spinfree Dirac equation and demonstratethat the resulting spinfree Dirac equations have different eigenvalues and eigenvectors.This means that the conventional division between scalar and spin-orbit relativistic effectsis arbitrary and depends on the method of separation. We also introduce an efficient wayto solve the full Dirac equation using the operators defined in the regular approximations.

95

P60

Screened self-energy and vacuum-polarization corrections to the 2p1/2 -2s transition of lithium-like ions.

V. A. Yerokhin1,2, A. N. Artemyev1,3, T. Beier4,5, G. Plunien4, V. M. Shabaev3 and G.Soff4

1Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany2Institute for High Performance Computing and Data Bases, St.Petersburg, Russia

3St.Petersburg State University, St.Petersburg, Russia4TU Dresden, Dresden, Germany

5Chalmers tekniska högskola, Göteborg, Sweden

A measurement of the Lamb shift in high-Z Li-like ions appears to be most promising fortesting QED up to second order in α. The accuracy of the best experimental results for the2p1/2-2s and 2p3/2-2s transition energy in Li-like uranium and bismuth [1,2] is by an orderof magnitude smaller than the second-order QED corrections. These results provide agood possibility for testing QED in a new region – the region of the strongest electricfield available at present for an experimental study.

We present ab initio calculations of the full gauge invariant sets of the self-energy andvacuum-polarization screening diagrams for the 2p1/2-2s transition in Li-like ions. Thecalculation was performed for extended nuclei in the range Z = 20-100. Variouscontributions to the transition energy are collected and a discussion of the totaluncertainty of the theoretical prediction is given.

[1] J.Schweppe et al., Phys. Rev. Lett. 66, 1434 (1991).[2] P. Beiersdorfer et al., Phys. Rev. Lett. 80, 3022 (1998).

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Participants

Steven AlexanderDepartment of Physics and GeologyUniversity of Texas Pan AmericanTX 78539 Edinburg, United States of Americatel: (1) [email protected]: P01

Dirk AndraeFakultät für ChemieUniversität Bielefeldpostfach 10 01 31D-33501 Bielefeld, Germanytel: (49) 521 1062086fax: (49) 521 [email protected]: P02, P46

Gustavo Adolfo AucarFacultad de Ciencis Exactas, Depte de FísicaUniversidad nacional de NordesteAv. Libertad 5500, Campus UniversitarioARG-3400 Corrientes, Argentinatel: (54) 3783 45846fax: (54) 3783 [email protected]: P03

Evert-Jan BaerendsTheoretische Chemie, Scheikundig LaboratoriumVrije UniversiteitDe Boelelaan 1083NL-1081 HV Amsterdam, The Netherlandstel: (31) 20 4447621fax: (31) 20 [email protected]

Maria BaryszDepartment of Quantum ChemistryInstitute of Chemistry7, Gagarin SreetPL-87100 Torun, Polandtel: (48) 56 6114761fax: (48) 56 [email protected]: S01

Thomas BeierDepartment of PhysicsChalmers University of Technology & Göteborg UniversityS-41296 Göteborg, Swedentel: (46) 31 772 3215fax: (46) 31 772 [email protected]: P60, S02

Paola BelanzoniDepartment of ChemistryUniversity of PerugiaVia Elce di Sotto , 8I-06123 Perugia, Italytel: (39) 75 5855526fax: (39) 75 [email protected]

Jacek BieronInstytut FizykiUniwersytet JagiellonskiReymonta 4PL-30059 Krakow, Polandtel: (48) 12 632 4888fax: (48) 12 633 [email protected]: P04, S03

Stephane BoucardLaboratoire Kastler BrosselUniversité Pierre et Marie Curie4 place JussieuF-75252 Paris, Francetel: (33) 144 274396fax: (33) 144 [email protected]: P06, P21

Maria Elena CharroDept. de Quimica FísicaUniversidad de ValladolidE-47005 Valladolid, Spaintel: (34) 983 423272/423208fax: (34) 983 [email protected]: P09

Chantal DanielLaboratoire de Chimie Quantique UMR 7551 CNRSUniversité Louis Pasteur4 Rue Blaise PascalF-67000 Strasbourg, Francetel: (33) 3 88 41 60 76fax: (33) 3 88 61 20 [email protected]: S04

Bert de JongPNNLMail Stop K1-83 P.O. Box 999WA-99352 Richland, United States of Americatel: (1) 509 375 3973fax: (1) 509 375 [email protected]: P10, P11

98

Maria Pilar de Lara CastellsDipartmento di Chimica Fisica ed InorganicaUniversità di BolognaViale Risorgimento 4I-40136 Bologna, Italytel: (39) 51 644 3698fax: (39) 51644 [email protected]: P12

John M. DykeChemistry DepartmentUniversity of SouthamptonUK-SO9 5NH Southampton, United Kingdomtel: (44) 1703 [email protected]: S05

Ephraim EliavSchool of ChemistryTel-Aviv UniversityRamat AvivIL-69978 Tel Aviv, Israeltel: (972) 3 6407634fax: (972) 3 [email protected]: P13, P33

Knut FægriKjemisk InstitutOslo UniversitetP.O. Box 1033N-0315 Blindern Oslo, Norwaytel: (47) 22 85 54 29fax: (47) 22 85 54 [email protected]: S06

Timo FleigLehrstuhl für Theoretische ChemieUniversität BonnWegelerstr.12D-53115 Bonn, Germanytel: (49) 228 735375fax: (49) 228 [email protected]: P14

Charlotte Froese FischerDepartment of Computer Sciencevan der Bilt UniversityBox 1679BTN-37235 Nashville, United States of Americatel: (1) 615 322 2926fax: (1) 615 343 [email protected]: P04, P17, S07

Laura GagliardiDipt. di Chimica Fisica e InorganicaUniversità di BolognaViale Risorgimento 4I-40136 Bologna, Italytel: (39) [email protected]: P16

Michel GodefroidLab. Chimie-Physique Moleculaire CP160/09Universite Libre de Bruxelles50 av. F. D. RooseveltB-1050 Brussel, Belgiumtel: (32) 2 650 3012fax: (32) 2 650 [email protected]: P17

Ian P. GrantMathematical InstituteUniversity of Oxford24/29 St. Giles'UK-OX3 7RY Oxford, United Kingdomtel: (44) 1865 273551fax: (44) 1865 [email protected]: P18, P43, P04, S08

Johan J. HeijnenTheoretical Chemistry, Materials Science CentreRijksuniversiteit GroningenNijenborgh 4NL-9747 AG Groningen, The Netherlandstel: (31) 50 3634393fax: (31) 50 [email protected]

Elsa S. HenriquesFaculdade de Ciencias, Dept. QuimicaUniversidade in PortoRua do Campo Alegre 687P-4169-007 Porto, Portugaltel: (351) 2 608 2827fax: (351) 2 608 [email protected]: P20

Bernd A. HeßLehrstuhl für Physische und Theoretische ChemieUniversität ErlangenEgerlandstr. 3D-91058 Erlangen, Germanytel: (49) 9131 85 27766fax: (49) 9131 85 [email protected]: S09

99

Ed A. HindsSussex Centre for Optical and Atomic PhysicsUniversity of SussexFalmerUK-BN1 9QH Brighton, United Kingdomtel: (44) 1273 678081fax: (44) 1273 [email protected]: S10

Jan HrusakJ. Heyrovsky Institute of Physical ChemistryAcademy of Sciences of the Czech RepublicDolejskova 3CZ-18223 Prague, Czech Republictel: (420) 2 66 05 34 [email protected]: S11

Paul IndelicatoLaboratoire Kastler-BrosselUniversite P&M CurieCase 74, 4 place JussieuF-75252 Paris Cedex 05, Francetel: (33) 144 274396fax: (33) 144 [email protected]: P21, P06, P47

Hans Jørgen Aagaard JensenDepartment of ChemistryUniversity of OdenseCampusvej 55DK-5230 Odense M, Denmarktel: (45) 65 57 2512fax: (45) 66 15 [email protected]: P22, P56

Uzi KaldorSchool of ChemistryTel Aviv UniversityRamat AvivIL-69978 Tel Aviv, Israeltel: (972) 3 6408590fax: (972) 3 [email protected]: P13, P33, S12

Mika KivilompoloDept. of Physical SciencesUniversity of OuluPL 3000FIN-90401 Oulu, Finlandtel: (358) 8 553 1330fax: (358) 8 553 [email protected]: P24

Werner KutzelniggLehrstuhl für Theoretische ChemieRuhr-Universität BochumD-44780 Bochum, Germanytel: (49) 234 7006485fax: (49) 234 [email protected]

Thomas La Cour JansenTheoretical Chemistry, Materials Science CentreRijksuniversiteit GroningenNijeborgh 4NL-9747 AG Groningen, The Netherlandstel: (31) 50 3634377fax: (31) 50 [email protected]: P28

Arie LandauSchool of ChemistryTel Aviv UniversityIL-69978 Tel Aviv, Israeltel: (972) 7396573fax: (972) [email protected]: P29

Yoon Sup LeeDepartment of ChemistryKAIST305-701 Taejon, South Koreatel: (82) 42 869 2821fax: (82) 42 869 [email protected]: P30

Wenjian LiuLehrstuhl für Theoretische ChemieRuhr-Universität BochumPostfach 10 21 48D-44780 Bochum, Germanytel: (49) 234 700 6673fax: (49) 234 709 [email protected]: P31

Pascale MaldiviDRFMC/SCIBCEA-Grenoble17 Rue des MartyrsF-38054 Grenoble Cedex 9, Francetel: (33) 476 88 53 03fax: (33) 476 88 50 [email protected]: P32

100

Gulzari MalliDept. of ChemistrySimon Fraser University8888 University DriveCND-V5A 1S6 Burnaby B.C., Canadatel: (1) 604 2913530fax: (1) 604 [email protected]: P33

Christel M. MarianInstitut für Physikalische und Theoretische ChemieUniversität BonnWegelerstraße 12D-53115 Bonn 1, Germanytel: (49) 2241 142536fax: (49) 2241 [email protected]: P14, S13

Laurent MaronLaboratoire de Physique Quantique, IRSAMCUniversité Paul Sabatier118, route de NarbonneF-31062 Toulouse, Francetel: (33) 5 61556836fax: (33) 5 [email protected]: P34, P50, P57

Thibaut MarrelLaboratoire de Physique des LasersUniversité Paris-Nordavenue J.-B. ClémentF-93430 Villetaneuse, Francetel: (33) 49403392fax: (33) [email protected]: P35

Tommi Olavi MatilaDept. Physical SciencesUniversity of OuluPL 3000FIN-90401 Oulu, Finlandtel: (358) 8 553 1317fax: (358) 8 553 [email protected]: S14

Spiridoula MatsikaDept. ChemistryThe Ohio State University100 West 18th AvenueOH-43210 Columbus, United States of Americatel: (1) 614 292 7806fax: (1) 614 292 [email protected]: P37

Markus MayerLehrstuhl für Theoretische ChemieTU MünchenLichtenbergstr. 4D-85747 Garching, Germanytel: (49) 89 28913603fax: (49) 89 [email protected]: P38

Jan MicankoSlovak University of TechnologyRadlínskeho 9SK-06601 Bratislava, Slovakiatel: (421) 7 593 25671fax: (421) 7 393 [email protected] .skabstract: P39

D. Michael P. MingosDepartment of Inorganic ChemistryImperial CollegeS. KensingtonUK-SW7 2AY London, United Kingdomtel: (44) 171 594 5754fax: (44) 171 594 [email protected]: S15

Wim NieuwpoortTheoretical Chemistry, Materials Science CentreRijksuniversiteit GroningenNijenborgh 4NL-9747 AG Groningen, The Netherlandstel: (31) 50 3634372fax: (31) 50 [email protected]: S16

Paolo PalmieriDipartimento di Chemica Fisica ed InorganicaUniversità di BolognaViale Risorgimento 4I-40136 Bologna, Italytel: (39) 51 644 3698fax: (39) 51 644 [email protected]: P12, P28, S17

Ann Marie PendrillDept of PhysicsChalmers University of TechnologyS-41296 Göteborg, Swedentel: (46) 31 772 32 82fax: (46) 31 772 34 [email protected]: S18

101

Grzegorz PestkaInstitute of PhysicsNicholas Copernicus Universityul. Grudzigdzka 517PL-87-100 Torun, Polandtel: (48) 56 6221065fax: (48) 56 [email protected]: P42

Pekka PyykköDepartment of ChemistryUniversity of HelsinkiP.O.Box 55FIN-00560 Helsinki, Finlandtel: (358) 9 19140171fax: (358) 9 [email protected]: P52, S19

Harry QuineySchool of ChemistryUniversity of MelbourneAUS-3052 Parkville, Victoria, Australiatel: (61) 3 9344 [email protected]: P43, P18, S20

Catherine RabbeCEA Valrho-MarcouleDCC/DRRV/SEMP/LCTSBat.166 - BP 171F-30207 Bagnols sur Cèze Cedex, Francetel: (33) 4 66791638fax: (33) 4 [email protected]: P44, P45

Markus ReiherTheoretische ChemieUniversität Erlangen-NürnbergEgerlandstraße 3D-91058 Erlangen, [email protected]: P46, P02

Sten RettrupDepartment of ChemistryUniversity of CopenhagenUniversitetsparken 5DK-2100 Copenhagen Ø, Denmarktel: (45) 35 32 02 81fax: (45) 35 32 02 [email protected]: P28, S21

Gustavo RodriguesLaboratoire Kastler-BrosselUniversité Pierre et Marie CurieCase 74, 4 place JussieuF-75252 Paris, Francetel: (33) 144 276300fax: (33) 144 [email protected]: P47

Norbert RoehrlNWFI - MathematikUniversity of RegensburgD-93040 Regensburg, Germanytel: (49) 941 9433341fax: (49) 941 [email protected]: P48

Angela RosaDipartimento di ChimicaUniversità degli Studi della BasilicataVia N. Sauro 85I-85100 Potenza, Italytel: (39) 971 474238fax: (39) 971 [email protected]: S22

Nino RunebergDept. of Chemistry, Lab.for Instruction in SwedishUniversity of HelsinkiPOB 55 (A.I. Virtanens plats 1)FIN-00014 Helsinki, Finlandtel: (358) 9 19140174fax: (358) 9 [email protected]: P49

Andrzej J. SadlejTheoretical Chemistry, Uniw. of Lund,Lund, Sweden andDepartment of Quantum Chemistry, Inst. of ChemistryNicolaus Copernicus University7, Gagarin StreetPL-87100 Torun, Polandtel: (48) 56 6114760fax: (48) 56 [email protected]

Bernd SchimmelpfennigMax Planck institut FKFHeisenbergstraße 1D-70569 Stuttgart, Germanytel: (49) 711 6891617fax: (49) 711 [email protected]: P50, P34

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Hubert SchmidbaurAnorganisch-chemisches Institut derTechnischen Universität MünchenLichtenbergstraße 4D-85747 Garching, Germanytel: (49) 89 28913131fax: (49) 89 [email protected]: S23

W.H.Eugen SchwarzTheoretische ChemieUniversität SiegenD-57068 Siegen, Germanytel: (49) 271 740 4338fax: (49) 271 740 [email protected]: S24

Luis SeijoDep. Quimica Fisica Aplicada C-14Universidad Autonoma de MadridE-28049 Madrid, Spain.tel: (34) 91 397 8724fax: (34) 91 397 [email protected]: P51

Vladimir ShabaevDepartment of PhysicsSt.Petersburg State UniversityOulianovskaya 1RUS-198904 St.Petersburg Petrodvorets, Russiatel: (7) 812 435 03 84fax: (7) 812 428 72 [email protected]: P60, S25

Jaap G. SnijdersTheoretical Chemistry, Materials Science CentreRijksuniversiteit GroningenNijenborgh 4NL-9747 AG Groningen, The Netherlandstel: (31) 50 3634861fax: (31) 50 [email protected]: P28, S26

Michal StrakaDepartment of ChemistryUniversity of HelsinkiP.O.B. 55 (A.I. Virtasen aukio 1)FIN-00014 Helsinki, Finlandtel: (358) 9 19140173fax: (358) 9 [email protected]: P52

James TalmanDept. of Applied Mathematics, Western Science CentreThe University of Western OntarioCAN-N6A 5B7 London, Canadatel: (1) 519 661 3649fax: (1) 519 661 [email protected]: P55

Christian TeichteilLaboratoire de Physique Quantique, IRSAMCUniversité Paul Sabatier118, Route de NarbonneF-31062 Toulouse Cedex, Francetel: (33) 5 61556836fax: (33) 6 [email protected]: P34, P57

Jørn ThyssenDepartment of ChemistryOdense UniversityCampusvej 55DK-5230 Odense M, Denmarktel: (45) 65 57 2580fax: (45) 66 15 [email protected]: P56

Anatoli TitovPetersburg Nuclear Physics InstituteGatchinaRUS-188350 St.-Petersburg, Russiatel: (7) 812 1495524fax: (7) 812 [email protected]: P41, S27

Valerie Valletlaboratoire de physique quantique, IRSAMCUniversité Paul Sabatier118, Route de NarbonneF-31062 Toulouse, Francetel: (33) 5 61556836fax: (33) 5 [email protected]: P57, P34, P50

Erik van LentheTheoretical ChemistryVrije UniversiteitDe Boelelaan 1083NL-1081 HV Amsterdam, The Netherlandstel: (31) 20 4447591fax: (31) 20 [email protected]: P59, S28

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Joop H. van LentheTheoretical Chemistry GroupRijksuniversiteit UtrechtPadualaan 14NL-3584 CH Utrecht, The Netherlandstel: (31) 30 2532733fax: (31) 30 [email protected]: S29

Christoph van WüllenLehrstuhl für Theor. ChemieRuhr-UniversitätD-44780 Bochum, Germanytel: (49) 234 700 6485fax: (49) 234 709 [email protected]: P58

Luuk VisscherAfdelingTheoretische ChemieVrije UniversiteitDe Boelelaan 1083NL-1081 HV Amsterdam, The Netherlandstel: (31) 20 4447624fax: (31) 20 [email protected]: P59, P33

Ulf WahlgrenInstitute of Theoretical PhysicsStockholm UniversityP.O. Box 6730S-11346 Stockholm, Swedentel: (46) 8 164620fax: (46) 8 [email protected]: P34, P50, S30

Vladimir YerokhinDept. of PhysicsSt. Petersburg State UniversityOulianovskaja 1, PetrodvoretsRUS-198904 St. Petersburg, Russiatel: (7) 812 159 4528fax: (7) 812 428 [email protected]: P60

Relativistic Effects in Heavy-Element Chemistry and...

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